What's a heatsink? Is it anything like a kitchen sink?
When it comes to the smooth operation of electronic components, cooler is better. The components prefer it, and so do the electrons carrying your audio signal - they don't jiggle about so much and therefore make less noise.
But electricity creates heat. So anything that works by electricity, including your recording equipment, will heat up. Whether this will cause a problem depends on what the equipment has to do.
In the early days of electronic equipment, heat wasn't that much of a problem. The equipment was fairly large and there was room for excess heat to dissipate directly into the air. Take tube guitar amplifiers for example. It is in the nature of tubes to get quite hot, but you don't need to worry about cooling. A little bit of breeze through the back of the cabinet provides all the cooling that's necessary.
But when transistor circuitry came into fashion, the reduced size meant that the heat become more concentrated. So transistors were, and still are, often fitted with heatsinks. On a small transistor, the heatsink is simply a piece of metal with fins to contact the air, and it just clips on. For power transistors, the transistor bolts onto a large multi-finned heatsink, preferably painted black as it radiates heat better.
For large power amplifiers, a heatsink by itself is not enough, and a fan must actively blow air over it, otherwise there will be a heat buildup and the transistors will destroy themselves.
Heat doesn't only build up in amplifiers. It also causes a problem in loudspeaker drive units. If a loudspeaker is driven too hard for too long, the voice coil will heat up and eventually at one point it will melt. After that, it won't work. So the voice coil is sometimes surrounded by 'ferrofluid', which transfers the heat to the magnet. In exceptional cases the magnet is fitted with a heatsink.
But the greatest heat problem these days is in the processor of your computer. These devices have to be small to be fast, but that creates an intense heat concentration. So the processor must have a large heat sink, which in turn is fitted with a fan.
Some processors measure their own temperature. And when they get too hot, they throttle back the clock speed until they have cooled sufficiently.
You'll notice when that happens due to a sudden drop in track and plug-in count. And you'll wonder what on earth is going on!
Ultimately more efficient techniques will be developed that don't create so much heat. But in the meantime we have to use heatsinks and fans. We don't mind the heatsinks, but the noise that fans make isn't exactly a good thing in the studio.
In conclusion, the world needs more efficient heatsinks. Either that or water cooling!