Given the high pressure at the contact point and the small size of the stylus, I would not be surprised if it does get hot. But, so what? It is in contact with any given part of the groove for so short a time there cannot be any significant transfer of heat. I don't know if there is some very short-term and very local melting at the point of contact. In any case heat is NOT an issue as to whether a record can be played again shortly after a playing.
What MAY be an issue is elastic deformation. When the record is played, the extreme pressure does cause the groove to temporarily deform. Like most elastic material when it is in such stretched state, the vinyl is also more brittle and is less able to further deform without tearing. The issue has to do with how long does it take for the groove to snap back to its original state.
It is evident for anyone who has repeatedly played the same track or part of a track that the groove snaps back to substantially the original state fast enough that one does not hear obvious distortion from a second play. Whether it has completely snapped back, and if not, whether the slight remaining deformation results in damage during a subsequent play is the issue. I read somewhere a long time a go that the record does not fully snap back for several hours. But, I don't think that records are so delicate and are being played so close to the margin for damage that it really matters, except perhaps, as an academic concern.
