I performed the suggested substitution. What is the heating up of money in that analogy?

Sarcastically, it's "the vibes intensifying".

(Vibes ~ Vibrations ~ Heat)

Tbf it's a reasonable question... I think it's a little tricky to pin down the equivalent of "kinetic energy" in purely economic terms, though you might look at the rate of flow of money as some analogy for the speed/energy of particles (speed of individual dollars changing hands). In that sense, the more frequent and larger these deals get, the hotter the market is. This is not a novel analogy.