Toyota Repair: 91 MR2, temperature thermostat, radiator cap

Question
I have a 91 MR2 non-turbo that I bought recently.  On the way home from picking it up it started to overheat so I towed it home.  I was going approx 80mph, 4000rpm on the highway.  I got it home and replaced the radiator cap because it failed a pressure test.  Two weeks later I was cruising near downtown and while I was waiting for a drawbridge to close it started to heat up again.  Got out and looked over the car, the fans were running.  Towed it home again and put a new thermostat in it.  It hasn't started to overheat on me yet since then BUT, every time I stop the engine, about 30 seconds after you shut it off, you can hear/feel the coolant boiling into the overflow bottle.  Are the fans supposed to stay on after you turn the car off?  You start the car back up while this is happening and the car doesn't overheat but it doesn't stop boiling either.  Should I go with a higher pressure cap?  A lower temperature thermostat (82c in there right now)?I don't want to drive it anymore until I get get this thing to run cooler.  Where should I start?  Is this a normal condition for this car? I don't have any experience with rear engine vehicles.  If you need any more info let me know and I can test the car.

Thanks.  

Answer
The fans are not supposed to run after the ignition is off.
You need to have it checked for a possible clogged up radiator or a leaking headgasket, I kind of suspect that it may have a headgasket problem so before wasting any more money on band-aid solutions go right to the worst thing it may be and either confirm or eliminate the headgasket as the problem, any repair shop should be able
to do a combustion leak test.
If the headgasket is not the problem suspect a problem with the radiator.