It does, but even if you keep the coolant temperature constant (thats all a cooling system does), internal components can overheat at high boost levels. Piston heads, valves and spark plugs are common failures since they are right at the source of combustion. However, the 5 minute restriction on the Merlin was a more of a maintenance limitation, than a failure limit.
On the DB 600 series of engines, oil was used for additional cooling of the piston heads, which is why you see larger and larger oil coolers on DB 605 powered aircraft like the 109G/K as higher boost levels were introduced. The main coolant radiators remained unchanged however.