1992 chevy C1500: Heat works on low speed, no medium, and high only works intermittantly.

Could be a number of thing's ! Testing the electrical circuit is the way to find out what's wrong . Using a wiring diagram and a DVOM - digital volt ohm meter . Videos on youtube showing how to test it ! Without testing i would only be guessing . Does it work in high speed ? In high speed it by-passes the resistor . If it doesn't work in any speed more then likely the blower motor is the problem !
Air Speed
The HVAC control assembly applies ground to the blower motor control circuit that corresponds to the selected blower speed. The resistors and the blower motor are in a series circuit. The following list represents the number of resistors in series with the blower motor per particular speed request:
• Low speed--3 resistors
• Medium 1 speed--2 resistors
• Medium 2 speed--1 resistor
When the operator requests High speed, the HVAC control assembly applies ground directly to the blower motor through the high blower motor control circuit. The resistor card has a fusible link which, if blown, will require that the card be replaced.

Blower Motor and Resistor Diagnostics by Wells

You mean the blower motor stops blowing air , the A/C compressor is still engaged ? The temp gauge shouldn't have anything to do with the blower motor .But stranger things have happened on these systems when they are controlled by a electronic module (BCM )
Circuit/System Description
The instrument panel cluster (IPC) displays the engine coolant temperature as determined by the engine control module (ECM). The ECM sends the temperature data via high speed GMLAN serial data to the body control module (BCM). The BCM then sends the information via low speed GMLAN to the IPC in order to display the engine temperature.
The BCM applies voltage to the blower motor through the HVAC relay. The resistors and the blower motor are in a series circuit. The following list represents the number of resistors in series with the blower motor per particular speed request:
• Low speed--4 resistors
• Medium 1 speed--3 resistors
• Medium 2 speed--2 resistors
When the operator requests High speed, the HVAC control assembly applies ground directly to the blower motor through the high blower motor control circuit.
Do you know anything about automotive serial data communications ? GMLAN Is general motors version of C.A.N controller area network .

How to Diagnose Controller Area Network CAN

Do you know anything about diagnosing automotive electronics ? Using a digital volt ohm meter ? Using wiring diagrams to pin point locations in a electrical circuit for testing ? Do you know what a factory componet location diagram is ? It takes more then looking at fuse's an relays , to see if current is flowing in a electrical circuit .

Electric Testing Techniques You Need to Know

ECM Inputs and Outputs Diagnosis

http://www.bbbind.com/free_tsb.html Free wiring diagrams ! Enter vehicle info. Year , make , model and engine size ! Under system click on HVAC , under subsystem HVAC Controls . Then click the search button , then click the first blue link . This is the blower motor control diagram . Do you know how to read a wiring diagram ?

RR/HVAC fuse 30amp located in the under hood fuse box. You can check it but highly doubt it's the problem . More then like it's the blower motor control module that's bad .
Circuit/System Description
The auxiliary blower motor is a variable speed fan. The HVAC control module controls the fan speed by sending a pulse width modulated signal to the auxiliary blower motor control module. The auxiliary blower motor control module varies the duty cycle across the auxiliary blower motor in relation to the pulse width modulated signal. The auxiliary blower motor speed can be adjusted from 10 percent to 90 percent duty cycle (PWM), 90 percent is high speed fan.
Watch this video for testing purpose's only , this is a front blower motor control module . Same way your back one works . GM is GM Chevy , Buick ,GMC , Cadillac .

The fuse box should be under the hood, passenger side. Try the upper box, middle right side Mine is huge, 30 amp

This vehicle doesn't have a blower motor resistor ! It has a blower motor control module , if you have automatic climate control !
If manual climate control , then there is a blower motor resistor assembly !
Blower Motor Control Processor The blower motor control processor controls the speed of the blower motor by increasing or decreasing the voltage drop on the ground side of the blower motor. The HVAC control module provides a low side pulse width modulated signal to the blower motor control processor over the blower motor speed control circuit. As the requested blower speed increases, the HVAC control module increases the amount of time that the speed signal is modulated to ground. As the requested blower speed decreases, the HVAC control module decreases the amount of time that the signal is modulated to ground.
Air Speed - Front Control
The blower motor forces outside air into the vehicle's interior. The vehicle operator determines the blower motor's speed when the driver places the blower switch in one of 5 blower speeds. The blower motor will always operate in any switch position other than OFF, as long as the ignition switch is in the RUN position. The blower motor and mode switches are located within the HVAC control module. The blower motor OFF input is connected in series with the HVAC control module by the off blower motor control circuit.
Depending upon the selected speed, power is provided to the blower motor from either the ignition 3 voltage or battery positive voltage circuits from the fuse block. The battery positive voltage circuit only provides power when the High blower switch position is selected. Power and ground are provided to the HVAC control module by the ignition 3 voltage and the ground circuits.
Low Blower Speed When the Low 1 blower speed is selected, the HVAC control module applies voltage to the blower motor resistor assembly through the low blower motor control circuit. Voltage is divided between 4 series resistors, a blower relay, and the blower motor to achieve the desired blower speed. The blower motor is grounded through the ground circuit.
Medium Blower Speeds When the Medium 1 blower speed is selected, the HVAC control module applies voltage to the blower motor resistor assembly through the medium 1 blower motor control circuit. Voltage is divided between 3 series resistors, a blower relay, and the blower motor to achieve the desired blower speed. The blower motor is grounded through the ground circuit.
When the Medium 2 blower speed is selected, the HVAC control module applies voltage to the blower motor resistor assembly through the medium 2 blower motor control circuit. Voltage is divided between 2 series resistors, a blower relay, and the blower motor to achieve the desired blower speed. The blower motor is grounded through the ground circuit.
When the Medium 3 blower speed is selected, the HVAC control module applies voltage to the blower motor resistor assembly through the medium 3 blower motor control circuit. Voltage is divided between a series resistor, a blower relay, and the blower motor to achieve the desired blower speed. The blower motor is grounded through the ground circuit.
High Blower Speed When the High blower speed is selected, the HVAC control module applies voltage to the blower motor resistor assembly through the high blower motor control circuit. The voltage energizes the blower relay, causing the blower motor to be connected directly to the battery positive voltage circuit. The blower motor and blower motor relay are grounded through the ground circuit.
Go on you tube an check out videos on trouble shooting blower motor circuit
Chevy Trailblazer EXT Blower Motor Won Turn Off

Did you test the circuit for B+ with a DMM - digital multi-meter ? Look at a wiring diagram to see all thing's involved ? Read in factory service info. how it works ? Without testing we'd only be guessing .
Air Speed
The HVAC control assembly applies ground to the blower motor control circuit that corresponds to the selected blower speed. The resistors and the blower motor are in a series circuit. The following list represents the number of resistors in series with the blower motor per particular speed request:
• Low speed--3 resistors
• Medium 1 speed--2 resistors
• Medium 2 speed--1 resistor
When the operator requests High speed, the HVAC control assembly applies ground directly to the blower motor through the high blower motor control circuit. The resistor card has a fusible link which, if blown, will require that the card be replaced.
Free wiring diagrams here

http://www.bbbind.com/free_tsb.html Enter vehicle info. Year , make , model an engine size. Under system click on HVAC ,under subsystem HVAC controls . Click the search button then click the first blue link , this is the blower motor electrical circuit .
Suggest u watch a few video's on youtube on automotive electrical testing .
Electric Testing Techniques You Need to Know

Which of these systems does your vehicle have ?
HVAC Systems - Automatic
Blower Motor Control Processor
The blower motor control processor controls the speed of the blower motor by increasing or decreasing the voltage drop on the ground side of the blower motor. The HVAC control module provides a voltage signal to the blower motor control processor over the blower motor speed control circuit. As the requested blower speed increases, the HVAC control module increases the amount of time that the speed signal is modulated to ground. As the requested blower speed decreases, the HVAC control module decreases the amount of time that the signal is modulated to ground.

HVAC Systems - Manual
Air Speed - Front Control
The blower motor forces outside air into the vehicle's interior. The vehicle operator determines the blower motor's speed when the driver places the blower switch in one of 5 blower speeds. The blower motor will always operate in any switch position other than OFF, as long as the ignition switch is in the RUN position. The blower motor and mode switches are located within the HVAC control module. The blower motor OFF input is connected in series with the HVAC control module by the off blower motor control circuit.
Depending upon the selected speed, power is provided to the blower motor from either the ignition 3 voltage or battery positive voltage circuits from the fuse block. The battery positive voltage circuit only provides power when the High blower switch position is selected. Power and ground are provided to the HVAC control module by the ignition 3 voltage and the ground circuits.
Low Blower Speed
When the Low 1 blower speed is selected, the HVAC control module applies voltage to the blower motor resistor assembly through the low blower motor control circuit. Voltage is divided between 4 series resistors, a blower relay, and the blower motor to achieve the desired blower speed. The blower motor is grounded through the ground circuit.
Medium Blower Speeds
When the Medium 1 blower speed is selected, the HVAC control module applies voltage to the blower motor resistor assembly through the medium 1 blower motor control circuit. Voltage is divided between 3 series resistors, a blower relay, and the blower motor to achieve the desired blower speed. The blower motor is grounded through the ground circuit.
When the Medium 2 blower speed is selected, the HVAC control module applies voltage to the blower motor resistor assembly through the medium 2 blower motor control circuit. Voltage is divided between 2 series resistors, a blower relay, and the blower motor to achieve the desired blower speed. The blower motor is grounded through the ground circuit.
When the Medium 3 blower speed is selected, the HVAC control module applies voltage to the blower motor resistor assembly through the medium 3 blower motor control circuit. Voltage is divided between a series resistor, a blower relay, and the blower motor to achieve the desired blower speed. The blower motor is grounded through the ground circuit.
High Blower Speed
When the High blower speed is selected, the HVAC control module applies voltage to the blower motor resistor assembly through the high blower motor control circuit. The voltage energizes the blower relay, causing the blower motor to be connected directly to the battery positive voltage circuit. The blower motor and blower motor relay are grounded through the ground circuit.

HVAC Control Module
The HVAC control module is a class 2 device that interfaces between the operator and the HVAC system to maintain air temperature and distribution settings. The battery positive voltage circuit provides power that the control module uses for keep alive memory (KAM). If the battery positive voltage circuit loses power, all HVAC DTCs and settings will be erased from KAM. The body control module (BCM), which is the vehicle mode master, provides a device on signal. The control module supports the following features:

fan motor most likely at fault, low speeds cause extra heat in motor

either the switch or there is a resistor pack in the heater duct that gets burned out and only 1 side works if it is not the high medium low switch check resistor pack mounted in the heater duct.

the blower switch is defective or the medium speed coil inside the blower motor is open(cut off). no worry if the low and high speed are still functioning