I can't speak to the mathematics of the heat generated during water jet cutting, but the following points may clarify the situation for you.
Heat affected zone is generally with metals where the cutting process will generate enough heat to change the mechanical properties of the metal, essentially locally heat treating the material at and nearby the cutting area.
Waterjet does not get near hot enough to create a heat affected zone. Remember, It's water at ambient pressure so it would become steam if it were any hotter than boiling temperature. That would make it an ineffective medium to carry the abrasive to blast through the metal.
Also, let's assume that the machine's water reservoir/supply is large enough where its temperature is stable. The pumping/pressurizing will create heat and the abrasive cutting action will create heat, but there is a "constant" supply of water at a stable temperature being applied to the material which would regulate the materials temperature.
That being said, a waterjet part could still become warm to the touch after being cut.