I have the opposite auto-stop issue than most other 2003 HCH owners.

It started a while back when I noticed the heat stopping to work at certain times for no apparent reason. Blowing cold air, when it was working fine a few minutes before. Engine temp is high enough at all times. Then it will start working again after a while. Today gave me the best hint. It is -20 outside and the heat stopped again and also the auto-stop kept coming on. When the heat started again the auto-stop would not come on in the cold temp (working properly). So it seems, by my logic, the thermostat that operates the auto-stop is also the same one that operates my in-car temp. It must be registering hot enough to start running cold air to cool my interior and also hot enough outside to start using auto-stop again. Just a guess but the best I can come up with. Does anyone know where this thermostat reader is located and if they are in-fact the same for both?

 

My guess would be you just have a problem with the heater. The dealership can go through the troubleshoot flowchart and sort it out.

One thing running only cold air into the engine compartment will accomplish is to make it easier for your engine to warm up, and stay warm (no coolant heat being drawn away to heat the car's interior), so there is a connection of sorts.