Radiator cap size

If it is up to temperature and you park it (shut engine off) then it pukes in to the over flow bottle from the cap hose it it is doing it's job, it will pull the water back into the engine.
The engine temps climbs fast after the engine is shut down..... is this happening as you drive under regular driving conditions as the engine is running ? If so,... on that radiator, I would think a 16 lb cap is fine to begin with, your old cap seal could be leaking and not sealing to the radiator