You seemed to be wondering why body heat might affect tempo but not pitch. Going along with your assertion that they're "essentially the same," my explanation is the difference in scale makes a slight difference in beat frequency much more noticeable than a slight difference in pitch.
That said I'm not sure I entirely buy your theory. It might work with unpitched instruments like drums, but what about say a musical phrase or chord with several different pitches? Or let's use light waves as an example: if you strobe a blue light fast enough, does it eventually begin to look red? Even if you played a drum beat 440 times per second, you would most likely get the same pitch, but it would end up being an odd continuous drumroll sound.