The brief
The C180 was running hot, the temperature climbing higher than it should. The owner stopped driving it and brought it in, which is exactly right with a car that's overheating. That points at the coolant pump. The pump circulates coolant through the engine and the radiator so the heat actually goes somewhere. When it fails, the bearing gets noisy, the seal weeps coolant, and the impeller stops moving enough water, so the engine overheats. On this engine the pump comes as a module with the thermostat, so when the pump goes you change the unit, which sorts a sticking thermostat at the same time. A failing coolant pump only gets worse, and an overheat can cost a head gasket, so it needs doing.
The diagnosis
A check of the cooling system traced the overheating to the coolant pump module, the bearing rough and the seal weeping, with the impeller not moving water properly, so the engine couldn't shed heat. The radiator, the hoses and the rest of the system checked out. That's a pump module replacement, with the integrated thermostat going along with it and a fresh seal, rather than chasing a weep that's only going to fail harder.
The work
The cooling system was drained, the old coolant pump and thermostat module removed, and a new genuine Mercedes-spec module fitted with a fresh seal and the drive belt set back up properly. The system was refilled with the correct Mercedes coolant, the air bled out the proper way so no pockets were left, and held under pressure to confirm the seals were dry. A road test confirmed the gauge sat steady through traffic and at speed with no overheating.
The outcome
Gauge steady, no coolant loss, the engine warming up on time, and no overheating. The C180 went home with the cooling system circulating properly again. A coolant pump that's noisy and weeping only fails harder, and the failure at the end is an overheat that can take the head gasket with it, so changing the module kept it to a tidy job.