Overheating

I have a Toshiba M35X-S111 laptop. The fan goes on at the beginning of boot-up, but then shuts off... and doesn't go on again. Basically the computer ends up heating up. Is this a problem with the fan or is it something else? If so... what would it be? I'm guessing something else as the fan works at the beginning so something controlling it staying on might be bad? I have a toshiba Satallite A105 laptop, it shuts down instantaneously without any warning or sign. I gave it to some repairshop thinking it would be the overheating problem, they said that they cleared up the dust and everything. Now the fan seems to run fine, I can hear it! but the problem came back after 4 days.. fan is still running fine! Don't know what is the problem now, sometimes it runs absolutely fine for 30-45 mins before shut down and sometimes it doesnt even boot properly and shuts down. Please suggest what could be the problem. Also, I thought may be it's my battery which is causing the problem cuz it;s worn out totally, so i tried running it by removing the battery and direct with the power source, but even that didnt help.. same issue!:(