The ACC sensor is separate from the temp gauge sensor. The temp gauge sensor is on the head between the #4 and #5 cylinders. It's a single post sensor. Pull off the wire and the gauge pointer will go limp. [On a W126] the ACC (105C/115C) sensor has a 2-pin connector and a single pin connector. The 2-pin connector has a constant ground wire and a wire to the Klima relay. The single wire goes to the electric aux fan circuit. When you hit 105C, the electric aux fans kick in full tilt. When you hit 115C, the compressor cuts off.
A bad 105C/115C switch is not uncommon but I think you have deeper problems if your car overheats in a few minutes while idling with the AC off. I can idle my 300SE a long long time with the AC off and the electric fans won't kick in.