FWIW, I live in NC andhave similar weather conditions during that time of year...I shoot year round and all my sight ins have been in the summer, hunt in the fall/winter...IMO, POI effects areeither inconsequential or don't happen at all in those minor differences in weather conditions.
I always get up early and am at the range shooting right at first light, which in the summer time here is usuallyaround 70*...then when I'm deer hunting in November, temps at first light range from the teens to the 40's...never had any indication there was a POI shift.

Sounds like the "jugs of water" approach would work...don't know if you use a hooked breech rifle or not...if so, a bucket might be helpful too...really, really need to get the bore& breechbone dry before plastering it with lube...maybe evenput thebreech end of the barrel on the floor with the heater blowing directly on it after cleaning to heat up the metal some...good luck with your season.