It's definitely an oil pressure problem. I'd be more inclined to think it is a leak if it operates well when cold. I'm guessing that once the thermostat for the oil cooler opens, oil is being lost somewhere in the hoses or cooler, reducing pressure to the rest of the system. Don't drive it like this.

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1977 300d 70k--sold 08
1985 300TD 185k+
1984 307d 126k--sold 8/03
1985 409d 65k--sold 06
1984 300SD 315k--daughter's car
1979 300SD 122k--sold 2/11
1999 Fuso FG Expedition Camper
1993 GMC Sierra 6.5 TD 4x4
1982 Bluebird Wanderlodge CAT 3208--Sold 2/13