You are good.
Copy/paste is a sequential process that runs the drive continuously.
It takes some 30 seconds for the drive to heat up to the point where it throttles.
At that point, it is a performance hit, not a dangerous thing.
Under normal conditions most of the activity will be small random I/O.
That is where the performance of a ssd shines.
Possibly your case cooling is suspect.
Take the case covers off and direct a fan at the innards.
If that helps much, look to better case cooling.
Really, though, you need do nothing.