For now lets assume the particle does not fracture into macroscopic fragments. Should a fate like that befall it then instead the methodology we create here can instead be reapplied for the fragments in question (with a lot of new variables that is).
How would one be able to determine the heat gained from air friction?
Also how would one be able to determine the transfer of heat into the "cooler" center of the sphere?
Obviously thermal conductivity comes to play a very large role here but even if the conductivity high is would it effect disintegration in the first (maybe few) second(s) at some non-negligible amount?