"I think liquid cooling is a thing in rocket science, "
The liquid cooling is for the combustion chamber and nozzle.
AFAIK no rocket turbines (which drive the pumps in most big rocket engines) are cooled. Jet engine turbine blades have been cooled for decades, which is why their operating temperature can be close (and sometimes exceeds) the melting point of the alloys they are made of.
Biting the hand that feeds IT
