Well, I'm not sure that magnetic tape is more susceptible to heat than film. The film base itself should be relatively stable. I'd worry about the gelatin emulsion on the film sagging or even melting from the heat as it has an upper heat limit of about 120 - 140 F.
Computer tape is Mylar with a ferric oxide coating (usually on both sides to prevent print through). The only thing that should be really susceptible to heat is the binder (glue) that holds the oxide coating on the Mylar backing -totally different than film.
Can you find out the internal temperature rating for the safe? Should be XX internal temperature after XX amount of time exposed to an external temperature of XX?