Blowing fan is running only in highest speed.

Check the bearings. If the friction is high the fan will not run at rated speed. When it runs slower it uses more current and gets hotter...

Disassemble, clean and lubricate to make sure fan runs full blast and does not burn out.

Or if the fan has two windings, one for starting and one for running it is possible that the high speed run winding has some shorts in it resulting in more current and more heat.

The fan speed relay is not working preventing the highest speed.

as far as the temp of the air blowing...it in direct proportion to engine coolant temp...try a hotter thermostat....as for the faan running continuously that is a seperate problem and sounds like a faulty rheostat or fan switch...rheostat is elect, switch on the fan motor that enables different speeds and may beinternal on your truck. only parts store will know . if it is replace fan motor. if not , test switch and then test rheostat

Fan speed control resistor block is the usual suspect for this. Quite in-expensive $10 - $20 ?
Easy to change, usually. Generally under the passenger side dash mounted in the air flow comming from fan. Maybe 2 - 3 screws on a block with a few wires, looking like it leads into the air cowling. May be behind glove box.
Do not run fan with new resistor out side of the air flow, it may burn out very quickly without the air blowing on it.

A heater blower motor resistor is an electronic device with three or more progressive resistors that allow the heater blower motor to operate at slower speeds. The highest speed of the heater blower motor is not controlled by the resistor, so when the resistor fails, the fan will often work on the highest speed setting, but not the lower speeds.
To resistor is generally located under the dashboard and under the hood, near the blower motor . The resistor's electrical connector is disconnected, the resistor is removed and the new resistor is installed. On some vehicles it may be easily accessible, and on others it may take partial dashboard removal to replace the resistor.
Look under the hood, generally the wiring for the Blower resistor is attached to the wiring to the blower motor itself
It's inboard & below the motor, near the accumulator. You can see it standing beside the passenger fender. it's the off-white connector behind the L heater hose above the vacuum reservoir & the white WARNING sticker

this is a smiple repair, replace the blower motor resistor, this is what controls the lower speeds and is very common,the resistor is locate in the heater box next to the blower motor.

From what you said I would think you have a bad/loose connection. I have never had to change the fan resistor but from what I under stand usually when the resistor is bad the fan only run with the fan speed on the highest setting. If the fan quits working try putting the fan on the highest speed setting, see if fan starts working. Sorry but that all I got for now.

The high blower works off a relay in the high speed only so the fan switch is at fault on your vehicle
Replace the fan blower control speed switch which is the one you adjust the lower fan speeds

Well it sounds like the blower motor relay is out you might also need a blower motor if it is using to much juice on high speed then the blower motor is probabley about to go out and with the noise you are describing it sounds like a bearing in the blower motor is about to go out so probabley should change the blower motor and the blower motor relay.

I would check the blower motor resistor. The resistor slows the current going to the blower motor to make the fan run slower for the first three speeds.The high speed runs of full battery voltage.I hope this helps.