Buy a SSD heatsink?
Data Hoarder
We are digital librarians. Among us are represented the various reasons to keep data -- legal requirements, competitive requirements, uncertainty of permanence of cloud services, distaste for transmitting your data externally (e.g. government or corporate espionage), cultural and familial archivists, internet collapse preppers, and people who do it themselves so they're sure it's done right. Everyone has their reasons for curating the data they have decided to keep (either forever or For A Damn Long Time (tm) ). Along the way we have sought out like-minded individuals to exchange strategies, war stories, and cautionary tales of failures.
Treat it like any other component overheating problem. Is there good airflow over the drive, or is it nuzzled at the bottom of your case between two hard drives and a rats nest of cables? Is it mounted on the motherboard back plate?
More info will let us help you more. What’s the temperature of the drive during these large file transfers? What’s the max temp before it powers off and is no longer detected?
Better cooling?
Try to transfer 500GB at a time and make sure you cool EVO with blowing fan at max speed? It's worth doing 250GB at time, you will probably get it done faster