@richardbrand @elliottbnewcombjr,
I recall advice that the same side should not be played immediately in order to give the vinyl time to recover its original shape.
Charles Kirmuss says wait 24 hours to play an LP again, they have to cool.
It's probably best not to play the same track repeatedly, but for the album, there is a 15-20 min delay before the same spot is replayed, and the how much is the record actually heating - very little.
The thermal conductivity of the diamond is the highest of all materials - ~1000 Watts/(meter-deg-Kelvin) - List of thermal conductivities - Wikipedia. Compare that to PVC or most other plastics - Plastics - Thermal Conductivity Coefficients (engineeringtoolbox.com) at <1-W/m-K). Additionally, the cantilever even if boron (~27 W/mK) which has the least of the various cantilevers (other than cactus) has a thermal conductivity much higher than the record. The diamond and cantilever are going to transfer the heat much faster and therefore heat much faster than the record.
Additionally, consider the record is moving between 51-cm/sec (510,000-microns/sec)-at the outer cut to 25-cm/sec (250,000-microns/sec) at the inner cut. If the stylus contact width is 2.5-micron, the stylus is in contact with the record at a spot 2.5-microns wide at most (2.5-microns)/(250,000-microns/sec) = 0.00001-sec (10 microseconds).
The amount of energy (watts) to produce heat can be no more than what is being used to spin the record - it's the conservation of energy, and as the record rotates, air is being moved which provides some cooling.

