Yet another factor: In practice, you don’t actually care about the ambient temperature of the air at any given spot. What you care about is how much heat will be transferred to or from your human body. Which means that you also need to worry about things like radiant heat, which will affect you but not the air.
Here is a video about how home water heaters work and have been made more efficient that (IMHO) has some relevant info, if not an answer the the OP’s question.
An important point in the video is - touch the tank. It’s barely warm to the touch. That’s how good the insulation is, which is why the tank can stay reliably warm for the daytime without heating. Do the same for your house walls (and ceiling, and floor) with sufficient insulation, and your house will leak very little energy. However, what it does leak cools the air and creates a convection flow. The cost of insulating (and especially retrofitting) trades off with the ongoing cost of heating to determine the optimum strategy. But in my newer house with 6-inch exterior studs and good modern (pink fiberglas) insulation, the corner room with outside walls cools off faster than the others.