The problem you describe is not uncommon with 190s. The TCC system in that car does require special test equipment to diagnose. Commonly this problem is caused by 1)a vacuum leak 2)a faulty potentiometer on top of the case which in a round about way causes no vacuum to reach the heater valve to close it. Also heater valves do go bad internally, which allows hot water to flow thru the heater core, AKA HEAT out side vents. Fortunately the heater valve on that car is inexpensive. If you physically pull up on the lever on the side of the heater valve and hold it closed for several minutes, the heat should diminish to none out side vents. The problem with your by-pass fix is, if you do not have a restrictor or a check valve in the vacuum line to the heater valve, when you accelerate you will dump the vacuum that is keeping the valve closed and you heat will momentarily come back.
It might be costly to diagnose and repair this problem, then again maybe not. Let your trusted MB tech find the problem for you, then make the decision yeah or neah.
Hope this helps,