Air continues to run with engine off

run fault codes and find out which sensors are faulty. The loss of power indicates that it is in limp home mode . Check oil level and coolant level at the radiator cap.

heater control valve shot

trysealing the system first then check the leval of freon before you add more

had a coolant flush lately? with ac on engine is loaded up and working harder. check thermstat operation make sure you have no restrictions in the front of the vehicle near the evaporator check your coolant flow is the engine in good working order

may just need cleaning with carb cleaner.

here is 1996, oldest I have:

Section 03-14: Engine Controls, Electronic 1996 Taurus, Sable Workshop Manual
REMOVAL AND INSTALLATION Idle Air Control (IAC) Valve Removal

1. Disconnect battery ground cable (14301). Refer to Section 14-01 .
   

1. Disconnect the engine control sensor wiring (12A581) from the idle air control valve (IAC valve) (9F715) at the idle air control valve electrical connector.
   

1. Remove the two idle air control valve retaining bolts.
   

1. Remove the idle air control valve and idle air control valve gasket.
   

Installation

1. NOTE: If scraping is necessary, be careful not to damage idle air control valve gasket surfaces, or drop material into intake manifold (9424) or throttle body (9E926) (depending upon application).
   
   Clean idle air control valve gasket mating surfaces.
   

1. To install idle air control valve, reverse Removal procedure.
   

1. Tighten the idle air control valve retaining bolts to 8-12 Nm (71-106 lb-in).
   

yes there is a blend air door that mixes a/c with the heated air and it sounds like it is out of adjustment the other thing is the heater core could be plugged

I was unable to locate code 31 in my book here is a copy of the codes. looks like you just need a fuse for #51. this may fix 31 as well.

Diagnostic Trouble Code Table 1994

AIR BAG DIAGNOSTIC MONITOR DIAGNOSTIC TROUBLE CODE PRIORITY TABLE
Priority Code Component/Fault Description
Highest - No Air Bag Indicator - Inoperative Lamp Circuit or No Ignition
Voltage to Air Bag Diagnostic Monitor

Continuous Air Bag Indicator - Air Bag Diagnostic Monitor
Disconnected or Inoperative
12 Low Battery Voltage
13 Air Bag Circuit Shorted to Ground
14 Primary Crash Sensor Circuit Shorted to Ground
21 Safing Sensor Not Mounted to Vehicle Properly
22 Safing Sensor Output Shorted to Battery Voltage
23 Safing Sensor Circuit Input Feed/Return Circuit Open
24 Safing Sensor Output Feed/Return Circuit Open
32 Driver Side Air Bag Module High Resistance or Open
33 Passenger Side Air Bag Module High Resistance or Open
34 Driver Side Air Bag Module Circuit Low Resistance or Shorted
35 Passenger Side Air Bag Module Low Resistance or Shorted
42 Center Radiator Primary Crash Sensor Feed/Return Open
44 Center Cowl Primary Crash Sensor Not Mounted to Vehicle Properly
45 Center Radiator Primary Crash Sensor Not Mounted to Vehicle Properly
51 Diagnostic Monitor Internal Thermal Fuse - Fuse Blown Due to
Intermittent Short to Ground
52 Backup Power Supply - Voltage Boost Fault
53 Primary Crash Sensor Circuits - Resistance to Ground or Air Bag
Diagnostic Monitor Failure

Lowest - Rapid Continuous Flashing of Air Bag Indicator (No DTC) All Primary

you need to make sure that the compressure is turing on when you turn on the a/c

the clock spring behind the steering wheel could be bad,about a $100.00 part through Ford

when you replaced all of that stuff on the vehicle did you make sure that you don't have a vapor lock in the highest anti-freeze line? to fix run vehicle with line disconnected so air can escape then reconnect. if that dont work you will need to put a T splice in the top anti-freeze line so when the vehicle is running you can open the valve and let air out.