The original oil cooler was an optional upgrade and most DR350's do not have them fitted. I've seen very few pictures of them. When Dr.Z posted his for sale on Adventure Rider, I grabbed the images...then later a few more photos from an eBay auction...then Bill Porter sent me photos of an installed oil cooler.
Here is some additional information from Bill Porter:
Before I got the oil cooler many years ago, I installed an oil temp gage. Without the cooler, I was surprised to find that the DR oil didn't get hot while running wide open climbing mountains on the highway while carrying a bunch of luggage. It got hottest by far at very low speeds - especially when slipping the clutch. In my opinion, the oil cooler seems to slightly reduce oil temp & the onset of clutch fade in very slow going. Unless you use synthetic oil, the cooler probably cools the oil too much at high speeds during the winter.