Most FM approved engine drive fire pumps do use heat exchange cooling using fire water as the raw water source. Also these packages, especially single engine pump systems, have no or minimal engine protection shutdowns, with maybe the exception of overspeed.
Have seen an engine damaged by reverse flow due to a check valve not closing, however was on a high rise building with a lot of head, and the supply water coming from a tank, so it had enough energy to rotate the engine backwards after it shutdown, resulting in damage to crankshaft and camshaft bearing. In those type applications normally you would also see a backstop to prevent reverse rotation.
In several systems I worked on over the years systems that tested regular into a "deadhead" circuit, had a shunt line to flow enough raw water to keep the unit from overheating.
FM1333 is the standard for diesel engines driving fire pumps, and is adopted in many countries.
To the OP, need way more info from you to make any kind of determination about your actual problem.
MikeL.