Sure, B&W films won't get colour-shift, but the film will fog anyway. I see no benefit to XP2 over a classic B&W; they're both sensitised silver halides, the only difference being that the XP2 has dye couplers in there to form black dye during development in C41. It's simpler than a colour C41 film by having just one sensitive layer instead of 3+ but it will suffer the same degradations as both B&W and C41 films. All films are sensitised silver halide at the root.
If the temps are bad enough to damage a roll of film during the span in which it might be loaded, it will be really bad for the camera+lens too.