Should thecooling fan continue to run after the engine is shutdown?

Problem:

The radiator is boiling over after shutdown when the temperature is in the mid 80's. What I noticed today: driving across town with the AC onandthus the AC fan running = no boil over after shutdown. On the return trip I shut off the AC just before entering my neighborhood = boil over immediately after shutdown. The boil over is coming from the reservior's overflow.

The AC fan is obviously reducing coolant temperature enough to mitigate the post shutdown temperature spike. We have had some recently chilly days and without the AC there was no overheating.

What I figure is the thermostat is not fully opening or the fan should be running longer ( or faster).

I bought the car twelve days ago and haven't had time to get a Haynes manual. It has 98273 miles.

Thanks,

Reg