I'm not a computer engineer, but I have done some research on this. So - take this with a grain of salt.
With nothing else going on, in theory: It takes the same amount of 'work' to 'handbrake' a file whether you do it at full speed or at a tenth of full-speed. The same of 'energy' is used, and therefore the same amount of heat is produced. At full-speed the heat builds up faster than it can naturally radiate away, and yes, your fans may need to kick up a notch. At 1/10 speed the same amount of heat is being produced, it's just being produced over a longer period of time, and some of it (or all of it, perhaps) will have a chance to radiate away before the fans need to kick up a notch.
It may seem that you use a tiny bit more energy to kick the fans up a notch... but as others have noted, the fans use a negligible bit of electricity. However, there is more. At 1/10 speed the CPU is not completely dormant. Its clock is still ticking, and its always checking to see what it needs to do next. It has a handbraking task in the queue, and it wants to finish it. Every clock cycle it's looping and checking to see if it's time to work on the handbrake job a bit more. Those extra loops and cycles also user up energy. So the extra tiny bit of power you save by not revving up the fans is more than made up for by the extra looping cycles as it waits to go to the next step.
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Why the car analogy doesn't work is because, among other things, you have air friction. The faster you push something through the air, the more turbulence you get ... which creates more drag. If your car was in a vacuum you would see much closer fuel economies... though there are other mechanical drags that increase with speed.