Its more likely to crash than run slow if the cpu fan is knackered. Best thing to do is find a mate whos handy with computers and get them to replace the fan and re-seat the cpu on the motherboard with some thermal paste between to get a better surface contact. Will help dissipate the heat better aswell.
Its more likely a collapse ball bearing in the case fan tho, replacing them is a 5 minute job and costs 5 quid tops.
I f**ks the hell out of me that these cons are ripping people off like that, my mate had a laptop and the graphics card went up the swany, they replaced the whole motherboard and RAM at a cost of 300 quid, i later found out it was becuase the ball bearings in the fan had collapsed causing it to overheat! Dont be fooled by these geeks in computer shops, always get a second oppinion....