You will not se a difference on consumtion or battery temp in normal temp or warm climates.
But in cold climates when it is cold, the heat pump use the heat energy in the battery to heat the cabin.
This reduces the consumption and increase the range.
I havent gotten all data for the Plaid yet, but I have it for my M3P ’21:
In cold climate if there is heat in the battery, the heat pump use it to heat the cabin.
If the battery is warm, from home charging in the garage or supercharging etc (or heated by dragstrip mode for the Plaid), the heat pump used the battery heat energy down to cell temp 12C.
After reaching 12C, the heat pump stopped takeing energy from the battery and used the lossy mode to heat the cabin if to cold outside to use air as the heat source, otherwise the outside air was used.
The battery slowly increased the cell temp to about 17C (from internal heating and heat loss from the motors) before the heat pump was allowed to use the battery heat energy again.
I havent really been able to see this yet on the Plaid, but we have about -10C now so after the next longer drive I can tell if the behavoiur is the same.
What I have done though is driving the same 250km drive in Plaid mode and Chill mode in AP, from about the same SOC, with the same tyre pressure in almost identical summer temperatures. The cell temps reached and stayed the same, and the consumption was virtually the same.
I did the same drive about one week ago and had some -5C to -8C, I did drive in Chill mode and the cell temp started at about 6 or 8C, as the car was charged with the UMC only at 2kW. The cell temp did only change very very little and very slow. It didnt rise to 17C, ever and it did not look like the heat pump ever used the energy. I just looked at the tablet with SMT from time to time but I have the logs, so it will be easy to check. I think it was not cold enough outside for the heat pump to need battery energy, and that it instead did use the outside air all the time.
For Winter or cold season, letting the heat pump suck the heat out of the battery down to 12C, if it does that would not be very vice in the Plaid mode. The power output would be bad with cold battery.
In the Plaid mode we can expect at least that the heat from the motors heat the battery, and that the heat pump is not allowed to use this heat for the cabin.
For the Chill mode, we can expect that the heat pump is allowed to use the cabin heat and that the cell temp will be clearly lower from this, with reduced consumption as the heat pump can use that energy. And that the motors heat heat the battery so this heat can heat the cabin.