As with most questions regarding computers, it helps to know the hardware you have. CPU fans can run full tilt for a number of reasons ranging from a dirty heat exchanger, using a three pin cooling fan, improper thermal compound and/or setting the fan speed to maximum in software/BIOS assuming your CPU utilization isn't maxed out. If you are referring to a laptop then the cooling fins are probably full of dirt. Get a can of air and blow out the dust and see if that helps.
As for the BSOD, it could be a number is things. Geno gave a good place to start but it could also be a bad motherboard, drive etc. It might be hard to diagnose without test equipment. Also, computer parts are so inexpensive nowadays it might be cheaper to systematically replace components than to pay a technician for diagnosis and repair.