That heat exchanger is the transmission fluid cooler, just so you know.
I should say that differently. It looks like the cooler used on an automatic transmission. Since the car is a diesel, then your mileage may vary.
You are describing conditions that arise out of the oil remaining cold too much of the time. Your trips are not long enough to fully heat the oil so that the water vapor that naturally exists can burn off. You partially warm the oil then park the car. This repeats day after day, and the water vapors accumulate and turn to a goo, that clogs coolers and creates problems of the sort you found. If I am correct on the transmission cooler, then you are doing the same thing to the transmission. The goo you found in the cooler can be condensation from the transmission fluid.
Part of the cause of these troubles is a short commute. If you get to work in 10 or 15 minutes, then you are making short trips that contribute to condensation in the motor oil. Your car is an '01, so one obvious take-away here is that it takes years of short commutes to make this problem come to a head.
jdstrickland, it's definitely to do with the engine oil. If you take a look at the last photo, of the housing you'll see two openings with a black rubber gasket ( top of housing) that's where the exchanger attaches. None the less I think you hit on an interesting point with the short trips as I grabbed a diagnostic app and hardware for the car a while back and pulled up an electric auxiliary water heater error ( the error still pops up now even after clearing). The car doesn't come up to temp in this cold weather and yesterday I surfed through topics on its failure and it mentioned the symptoms I'm experiencing, so you could very well be right ( in a round about way) about the gumming up on the water side due to the oil not getting up to temperature. This error doesn't signal a warning light so god knows how long it's been faulty for. Thanks for the input!