P.S. - If it is the sending unit, you might consider a manual oil pressure gauge with copper tubing. Much more accurate than an electrical sending unit. I am installing mine this weekend cuz my sending unit is shot and my gauge reads 60-80 psi!
Have you considered the oil pressure sending unit? It may be faulty. Coincidental cuz of the cooling problem, but it might be shot... The gauge would become eratic if the sending unit failed.