What could be the problem in a 1987 Chevy Celebrity when the check engine light comes on after it idles for about 10 minutes?

I had the same problem. The cooling fan wasn't running, so the engine over-heated. The lever (bi-level, a/c, defrost, etc) needs to be on so the fan will engage. The fan is tied into that system. one of a few things it could be.. "sensors" if you pick up a book at a part store it will have values of all the different sensors in it .. by hooking up a simple ohm's meter u can check the values if there off more than .01 -.05 it's going to be a bad sensor u can use this on pretty much all gm and ford sensors if i had to guess i would say start with a coolant temp sensor it's the sensor just below the water inlet housing ....