Yes, having the heat on can cause the ICE to be on. If you have the temperature set to higher than that of the outside temperature, it can cause the ICE to start to create warmth. At 52 degrees, if you had the heater on, it might be the cause of the ICE starting. I have tried this out when sitting in a drive through. I noticed that as I turned the heat down, the ICE would shut off.

Also, I have found that the ICE will be on after I have driven 15 highway miles and then driving in my subdivision. When it is warm outside, the ICE usually shuts off, but when it is colder, it does not. However, even when the ICE is on when driving in my subdivision, the MPG readout shows 60 MPG.

I think there are several factors at work. One is the climate control system. Another is maintaining the ICE's normal operating temperature. A low SOC can cause the ICE to be on. Like I said above, my TCH's ICE will come on after a good drive and the SOC is green, with only the top bar not filled (by the way, I have only been able to get the top bar to fill after a long downhill coast on a highway. I have had my TCH since April, and this is the only time it has happened). I am sure there are other factors as well. Or a combination of those above. I would try to turn off the climate control and see if anything changes.

Best of luck
Jason