Confirmed from the FSM (DVD version) -- USA versions of the 1997 E300D have an oil-to-coolant cooler. Maybe they went to an oil-to-air cooler in 1998 and tried it out first in Europe and the UK in 1997.

FYI, my 1987 300D Turbo (W124, OM603) has an oil-to-air cooler like yours, left side of the engine bay, low down like your pictures.

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"Buster" in the '95

Our all-Diesel family
1996 E300D (W210) . .338,000 miles Wife's car
2005 E320 CDI . . 113,000 miles My car
Santa Rosa population 176,762 (2022)
Total. . . . . . . . . . . . 627,762
"Oh lord won't you buy me a Mercedes Benz."
-- Janis Joplin, October 1, 1970