The brief
Kenneth brought his 520i in for a service and mentioned the engine temperature had been running a little higher than usual. A gauge that sits a touch high is the early warning, the time to look before it becomes a proper overheat, so two jobs in one visit: the service, and the cooling. The coolant pump circulates coolant around the engine and through the radiator, and the thermostat controls when that flow opens up. As both age, the pump moves less coolant and the thermostat doesn't open as cleanly, so the engine runs warmer than it should. And the fan belt that drives the pump had a crack starting in it, which matters because if it breaks, the pump stops and the car stalls out hot. Worn cooling parts don't recover, so the pump, the thermostat, the belt and the tensioner all got renewed.
The diagnosis
On the ramp the sharp-eyed check found the fan belt cracking and worn, and the coolant pump and thermostat past their best, which together explain the slightly high engine temperature. The radiator and the rest of the system were sound, and the belt tensioner was due alongside the belt. That's a coolant pump and thermostat replacement, plus a new fan belt and tensioner, with a coolant refresh, rather than waiting for the warm running to become an overheat.
The work
The cooling system was drained, the old coolant pump and thermostat removed and new genuine BMW-spec units fitted with fresh seals, and the cracked fan belt and the worn tensioner replaced and the belt tension set to spec. The system was refilled with the correct BMW coolant, bled the proper way so no air pockets were left, and pressure tested. The service items were done alongside. A road test, including time idling in traffic, confirmed the gauge holding steady, the belt running true, and no warm running.
The outcome
The temperature gauge holding steady on the move and in traffic, the fan belt running true on a fresh tensioner, the coolant fresh, and no warm running, with the service done. Kenneth got the 520i back running cool. Catching the worn belt and the tired pump and thermostat at the service meant they were dealt with before the warm running turned into an overheat, which is the cheap way to handle it.