Fuses 19 and 30 on my car control the gauge cluster. By disabling the gauges, the car cannot read the coolant temp and defaults to 106C. Of course, your 97 might be different.
The reason I suspect something with respect to the fan is that my electric fan runs at a slow speed most of the time in the summer. Never looked in the winter.
Without the fan running, you're not pulling enough air through the rad or the condensor.
The evap temp sensor has nothing to do with the movement of the car, and that I would imagine rules it out, as your AC blows cold when the car is moving.
Things are pointing to a fan problem. No slow speed fan engagement would cause the problem set you have.
1998 C230 "Black Betty"