Not long ago I needed to examine 20--30 rolls of 35mm Plus-x and Tri-x that had been stored since 1967 in the attic of a barn in Alabama, rolled tightly and wrapped in paper. The film was wound into rolls about the size of my thumb, and wanted to stay that way. In order to get them into a scanner, I cut each roll into strips, and used pieces of scrap mounting board to hold them flat on a larger piece of mounting board, with tape keeping the assembly together (but not touching the actual film). The whole works went into a warm dry mounting press with barely enough pressure to hold things snugly; the press was heated just really warm to the touch, and then powered off. After the press had cooled (an hour or so) the film came out flat and (amazingly) entirely undamaged.
I can't say that I would recommend this for anything important, but in this case it was sort of a last-ditch effort, since the film was so curly that it was almost impossible to examine with a loupe, and getting it into a negative carrier would have been even more likely to damage it. It was probably fortunate that the film had been in a low-humidity environment for months before I tried this; I suspect that in Alabama humidity it would have picked up texture and/or particles from the mounting board. If I absolutely had to do something like this on good film, I think that I would use strips of very clean silicone release paper to protect the negatives, and make sure that everything was good and dry before starting.