[Solved] Does a computer perform better at lower temperatures

The performance of the system is controlled by the clock speed - temperature itself won't change the speed of your system. But a temperature that's too high can affect system reliability and longevity.

If you want to overclock your system (increase the clock speed to run faster than the value specified for your CPU), then the system will run hotter and at some point the CPU will become unstable and crash. If you have better cooling equipment then you'll be able to keep the CPU cool enough to run reliably at a higher clock setting.

But it's not the cooling equipment itself that makes the CPU run faster, it's the clock setting that directly controls the CPU speed. The cooling equipment is just there to keep the CPU from getting too hot to run at that speed.