No.
However, playing games stresses CPU and video and when that happens they produce heat. If your PC is not properly ventilated, or the thermal compound between the heatsink and those components is deteriorating, then you will have excessive heat which can cause damage to your PC.
FS '04 will only use 1 core since it is not multi-threaded, therefore if you have a 3.0Ghz dual core and a 2.6 quad core computer, FS '04 will play faster on the dual core.