2002 pontiac grand prix se runs hot going up mountains

It runs hotter because the engine is working harder or, in the case of slow traffic its not getting a good supply of cool air through the radiator. That's normal. As long as its not overheating everything is fine. Make sure your coolant level is at the full mark and motor on.

Check radiator when cold. Reserve overflow tank is not the one to check. My fluid went down for years until I found the plastic fittings in hoses by the thermostat were cracked and you couldn't see water leaking. less than $5 to fix.