Gateway 2.4GHz PC running WinXP SP2.

I noticed a few days ago that when I put my PC in standby mode the CPU fan will continue to run for as long as there is power to the machine. If I shut the machine down, of course it stops. A buddy suggested the temperature sensor may be failing/failed, but how do I know for sure, and if it is, what can I do about it?

I opened the case and vacuumed the dust out about 2 months ago, doing so I also removed the CPU fan and heat sink to clean all the gunk out. I didn't remove any of the heat transfer paste, but could it be that I need to apply more? Is it possible that my cleaning may have affected the cooling ability and it has slowly wrecked my processor?