The heat come on turn off but fan will not shout off.

Sounds like a fan relay is stuck. Check out pictures of this part on sites for Autoparts. Yours may be next to Radiator fan. Now if fan eventually stops, some are made to cool engine compartment once car is parked as heat builds up for a period of time once the engine has stopped.

when was lat time serviced --tuned up or cleaned --

Check compressor working and also gas pressure. Please confirm heating sensor is.o.k.

sounds like the wires are messed up check see if the dash main power wire is touching something grounding out or see if the fuse is messed up and passing current when not supposed to be

may be the relay is stuck, you will need to open the unit and see if the relay is releasing when you turn off the breaker. hope this helped tim

There is well-established procedure for trouble shouting the over heating.
Does the car overheat in driving mode?
Yes.
Are you losing coolant?
No. Check water pump (including belt) and thermostat.
If yes make a radiator compression test. You might have a bad cylinder head gasket.
The car doesn’t overheat in driving mode, but overheat in idle.
Does the fan runs?
No.
Check the fan assembly for a bad motor, loose fan blades, or bad connector.
Check the codes for a bad temperature sensor.
Check cooling fan relay and fuse.
If this isn’t enough to solve problem, then send the car at dealer for a “check and advice”.

As a saftey feature on newer pcs manufactures have equiped desktops and laptops with heat sensors. It sounds to me that the cpu is overheating. If this is a desktop, remove the side cover and clean all the fans, and check for dust build up on the cpu heat sink. If this is a laptop inspect the vents on the rear and bottom for dust or obstruction. Hope this helps ;)

sounds like the oven heating element is defective, shout be about $150 to repair, less if you do the work

It seems that you are saying the thermo fan stops first, thenfotre the safety limit switch shouts off the gas. This would mean the thermo fan motor is bad. It is overheating, which cuts out the thermo fan switch. The gas only shouts off because the thermo fan motor is bad.