Yes, I think you maybe over analyzing , the mass of the stone is about 1,000 times less the mass of a body , so it will not noticeably change the body temp, if it did more sweat would be produced to bring the body temperature down...
82.93 x 0.198 = 16.2 ... every degree C drop in temp liberates 16,2 Cal.
The stone went from 84.5 to 37 = 47.5 degrees x 16.2 = 769.5
The body absorbed 769.5 calories of heat
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