This depends on the vehicle, and if there is a system pressure relief valve and what that might be set to begin relieving pressure.

The 190E 2.3-16 engine has a higher capacity pump and it, regardless of oil temperature (and it has an oil temperature gage) is always pegged at the 3 bar mark. This engine has a relief valve built into the oil pump housing.

I am not sure the W123 616 or 617 engines have such a device. At any rate, the pump outlet goes to the filter housing. In the filter housing there is a thermostat that diverts flow to the radiator when the oil gets hot. When the oil is not hot, the oil bypasses the oil cooler flow path, and goes directly to the OD of the replaceable filter element. This volume is always connected to the oil cooler (it is where the return flow goes to the filter), so, the oil cooler is always at the pressure of the OD of the oil filter, which is going to be the pump discharge pressure and that varies based on temperature.

The pump discharge pressure, based on the wall thickness of the filter housing, isn't too high. It is likely highest with cold oil, since the pump is a positive displacement type pump and the flow rates with cold oil generate more resistance which demands greater pressure and the positive displacement pump is happy to provide it. Which how the oil selection for winter can be critical for getting the starter to spin the engine fast enough to start.

I hope this helps. Jim

__________________
Own:
1986 Euro 190E 2.3-16 (291,000 miles),
1998 E300D TurboDiesel, 231,000 miles -purchased with 45,000,
1988 300E 5-speed 252,000 miles,
1983 240D 4-speed, purchased w/136,000, now with 222,000 miles.
2009 ML320CDI Bluetec, 89,000 miles

Owned:
1971 220D (250,000 miles plus, sold to father-in-law),
1975 240D (245,000 miles - died of body rot),
1991 350SD (176,560 miles, weakest Benz I have owned),
1999 C230 Sport (45,400 miles),
1982 240D (321,000 miles, put to sleep)