As Stu says, the way in which the curved rails are formed will have a very significant effect on its reaction to the fire. I wouldn't imagine that there's any particular reason why a piece of timber machined into a curve would bow any more or less than a straight piece, so long as they were cut from the log in the same way (quarter-sawn, half-sawn etc). I agree with Stu about the steamed timber. It could conceivably be laminated rails, too, in which case if the glue melts it'll all fall apart! Intumescent strips could also make the distortion worse, if they are high pressure types, although at 50mm the rails may have enough strength to resist the bowing tendency, for a reasonable period of time.
I don't know of any models that predict the performance of timber doors when exposed to fire from 'first principles', but there are well-established techniques that extrapolate the performance of tested constructions (e.g. increased height, width etc...).