Radiator fan only turns on when my car is off?

I'm going to a mechanic tomorrow, but I'd like to have an idea of what the problem is before I go in, so they don't overcharge me for repairs I don't really need.
I have a 1992 honda accord. It has a lot of problems, but has been, for the most part, drivable. I've had problems with the fan in the past; it doesn't turn on when my a/c is on, so my car will overheat. I pretty much just ignored that though (would rather save money for a new car than spend it on a repair that isn't 100% necessary) so I just don't use the a/c. But today, I noticed my car overheating while driving. A/c was not on. So I pulled over, checked the antifreeze, etc. After playing around with it for a bit, I noticed that the radiator fan only turns on once the car is off. So the fan itself is still functional, and when the car is off, it recognizes that it's too hot. But when the car is on, the fan will not turn on, no matter how hot it gets. What do you think could be the problem?

Check the temperature control module. Sounds like it may be going bad.

The fan control switch is on the thermostat housing. Unplug the wires to it and jumper them, turn the key to the run position and if the fan works replace the switch.

A strange problem but If it was mine, I would pull the wires from the fan and run it off the ignition switch. That way it will be on all the time and cooling all the time. The only harm done will be that there will be slightly less gas mileage (very little) and slightly more strain on the alternator. You will probably not notice either.

I'm not familiar with Honda. But some part of the temperature sensing device isn't working. Maybe it became miscalibrated, and only turns on when it's really hot, which it will get after you shut the engine off. Just tell the guy that the fan works, but only when the car is not running. It's probably just the temperature sensor. If he wants to install a new fan, tell him no.