Certainly any part can fail - however, thermistors are fairly reliable and fairly stable, but they can change over time. If you have another mainboard, (maybe a friend) test your heatsink and cpu on their board. It works ok, probably an bad thermistor, replace mb(repairs will cost more than replacement). If it fails there also, then problem is bad heatsink or cpu. Fan could be crapping out (turning but much slower) or cpu could have shorted out in some part of the die area causing to draw too much current and therefore heat rapidly. But it would certainly point to one of those three components. Gettitng a way to test them can be a problem. I was having a similar problem (almost identical), I had bought all a Fry's. So I took all three in, and had the tech test them, which they did for no charge (probably because the mainboard was bad and still in warranty).
btw Eagler is right, prices as they are today , a new chip AND mb are less than $150, and quickly be "cheaper" than the time spent trying to figure it out.
