Idling problem Audi A6 2.6 V6 1996 Petrol

can't help on the climate control, but the cold idle problem is classic of bubbles in the coolant [because if there's insufficient to be always covering the main coolant sensor, the signal to the engine computer fluctuates and the computer adjusts idle speed according to the sensor reading fluctuation]. check inside the radiator, not just the expansion bottle, and ensure the level is ok. if you're lucky, you're just a little low. if you're not, your head gasket is starting to go and exhaust is bubbling through - a coolant chemical ["bromothymol" blue] test will confirm.

can't help on the climate control, but the cold idle problem is classic of bubbles in the coolant [because if there's insufficient to be always covering the main coolant sensor, the signal to the engine computer fluctuates and the computer adjusts idle speed according to the sensor reading fluctuation]. check inside the radiator, not just the expansion bottle, and ensure the level is ok. if you're lucky, you're just a little low. if you're not, your head gasket is starting to go and exhaust is bubbling through - a coolant chemical ["bromothymol" blue] test will confirm.

Looks like there are three total. One for the cooling fans, one for the gauge and one for the ECM.

One is in the coolant crossover tube, another is behind the thermostat housing while the third looks to be on the back side of the intake. The image I have is real crappy but that is where the part listings show.

as steve says, there are three sensors. the gauge sensor is "dumb" and doesn't do anything else. the fan "sensor" is really just a switch. and the ecm sensor, the main coolant temp monitor, drives everything else, including the climate control input. it's clearly working or you'd be getting a check engine light and you'd have told us that [right?].

so, since you haven't looked at the radiator coolant level, you haven't done the chemical test, you've not done anything like look for bubbles in the expansion bottle, or done a coolant system pressure test, and the symptoms you're describing are typical of early stage head gasket failure, particularly for a vehicle this old, my money is on gasket failure denial.

as steve says, there are three sensors. the gauge sensor is "dumb" and doesn't do anything else. the fan "sensor" is really just a switch. and the ecm sensor, the main coolant temp monitor, drives everything else, including the climate control input. it's clearly working or you'd be getting a check engine light and you'd have told us that [right?].

so, since you haven't looked at the radiator coolant level, you haven't done the chemical test, you've not done anything like look for bubbles in the expansion bottle, or done a coolant system pressure test, and the symptoms you're describing are typical of early stage head gasket failure, particularly for a vehicle this old, my money is on gasket failure denial.

Even if other things (radiator cap, recovery tank, hoses ...) are functioning normally, you can still have a low coolant level in the radiator while the recovery tank remains full if there's a leak elsewhere in the system (such as a leaking head gasket) that allows gases to be pulled into the coolant system instead of coolant being pulled in from the recovery tank.

good luck. if you /are/ lucky, i'm completely wrong. hope so.

he can't look at the radiator coolant level without disassembling half of the car

there is no radiator cap on my a4 and I assume there was no one on a6 back in 1996

the "overflow" tank is pressurized with a (plastic!) screw cap on top