Short of running next to no oil or a significantly thicker grade then recommended (esp. in cold weather), you shouldn't have to worry too much about a Honda/Acura oil pump.
It's used, so you never know, but I'd try several other things (fixing the leak being first on the list of course) before even considering that as the problem.

Not saying you're wrong, but if it was low oil pressure causing excess heat, you'd expect the oil light to be on.