Maybe. Does anybody have fiber insulation between the firebricks and firebox steel? Even if this were the case it gets mighty hot at the actual firebox. Fire is at over 1000 degrees. The ambient air at 25 vs 65 is just not important to the firebox but I do believe it will cool the heat exchanger quicker. Enough to cycle the blower.
I feel like you’re imagining a wood boiler with perpetually 33 degree water jacket around the firebox. A warm air furnace is not like that. The still air around the firebox will quickly warm until it’s hot enough to be whisked away by the blower. Cold air is much less able to steal heat from the firebox than water. Imagine quenching a hot piece of metal in a bucket of water compared to waving it around in the air.
I could very well be wrong, but it's a concern I would have for sure. Doesn't take much moisture at all to get trapped and to start the rusting process. Once it starts, it's over with. I would definitely make sure my low limit snap switch was set appropriately to keep the temps up inside the air jacket as much as possible.
I don't think I would be too concerned. It's an issue with boilers but they have liquid cooled fire boxes.