I'm not all that familiar with W124's. Is there a heat shield "between the air filter and the rest of the engine"?

It sounds like the shield that's right below the air cleaner on a W-123.

In my picture, the air filter goes to the right of the red arrow, over the air intake pipe (black tube with hole). The aluminum piece that the arrow points to is not specifically designed as a heat shield but does block some engine heat, especially radiant heat from the exhaust manifold, trap cat, its later replacement, the turbo, and the down pipe. The air filter case in a W124 is plastic as is the coolant expansion tank. (Both have been removed as part of the work that was going on when I took that picture last year.)

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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