can heat slow down your computer?

In short answer yes
You might also hear the internal fans working faster, more noisily, than usual; your computer will try to cool itself down by venting higher temperatures via the heatsink (a naturally-heat conductive component typically made of aluminium) and the accompanying fans which direct CPU heat through the case.

Computers have a fail-safe which shuts down overheating parts to prevent permanent damage. In some instances, the whole system will shut down and refuse to fully restart until it has sufficiently cooled. Even then, if there is malfunctioning hardware, it might allow you access to files briefly before shutting down again.
 
CPU's and gpu's will throttle if they get too hot and if the cpu keeps getting hotter even after throttling it will hit a point where it will shut the pc down. Computer and high temps is bad. The idea is to have adequate cooling so it doesn't get to this stage at all. If your pc was ok at some point and is now overheating then either a cooler or fan(s) have failed or it's full of dust. You can download software such as HWMonitor and many others to monitor temps.
 
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