92 Accord - cooling fan problem

Hi,
I have searched this forum and could not find answer to this problem. Recently I have noticed that the cooling fan comes on after truning the engine off more frequently. It used to run for a few minutes after a long drive. But now it starts after every short drive too. But it stays on just for a few minutes. The temperature dial doese not go over the middle range. I also noticed that when the car is hot and I stop for a short period of time, it starts and dies immidiately. If I try to start, it will crank but won't start . It does start after a few minutes though, I mean I have to wait a few minutes.
My distributor cap/rotor and fuel filter have been replaced. I am thinking that may be the thermostat is not functionaing to its 100% efficiency which causes overheating enough to cause these problesm. It might fail in the near future. I admit I might have multiple problem.

I would really appreciate if a kind soul could shed some light on this problem. Thanks
Davood

As for the starting problem, it could be the main relay. 90-93 accords have problems with the main relay, it's a $40 part at Auto Zone, you could also try ebay. And the cooling fan problem I'm going to guess at, it could be that the Radiator Fan Sensor could be giving falty readings and telling the fans that the engine is hotter than it actually is. I'm just taking a shot in the dark at that though.