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.
I have the same drives with the same problem. I took them out of the ssd case and put an m.2 thermal pad on them(the side of the pcb with the controller) and a 10C australian coin on top of the thermal pad. Replaced the case and now the 10c coin is pressing against the plastic ssd case slightly transfering heat much better outside the ssd case.
Thermal pad without the coin would probably be fine too, as long as it's making contact with the outer plastic case and the controller/flash chips.