Well, for one thing, MB engines are not designed to operate without a t-stat.

All you end up doing is short circuiting the radiator.
Look at the manual, there is a flow description.

The aux pump is irrelevant wrt cooling. It's only there to boost flow into the heater core at idle. Not all MBs are equipped with aux pumps.

Perhaps you have a head gasket problem? Your description of the heater output suggest that this may be a possibility.

Jim

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14 E250 BlueTEC black. 45k miles
95 E320 Cabriolet Emerald green 66k miles
94 E320 Cabriolet Emerald green 152k miles
85 300TD 4 spd man, euro bumpers and lights, 15" Pentas dark blue 274k miles