The fan blows cool air into the grooves of the heatsink; hence the term air cooling. The air removes the heat from the heatsink. The thermal pad acts as a transfer for heat from the CPU to the heatsink, so it is important. But, a CPU won't explode just because the fan quit. First of all, you may be able to hear whether the fan is turning or not. Second, if the fan fails, and you boot the computer, the computer will reset after a few minutes. If you leave it powered up for a long time, however, the CPU will burn out.
Usually, a CPU will not just "explode", unless "overclocked to ze extremz". A CPU without a HSF will merely burn out, literally. The ciruits in a CPU are so tightly packed, there is no room for the heat created by electricity to escape.