It has been a while since I took thermodynamics in collage, but I think this is close.
There are 3 components that contribute to thermodynamics. They are conduction, convection, and radiation. For a bee hive I think conduction would be the main mechanics for heat loss in a hive. The differential in temperature between the hive and outside air is probably low enough that convection is fairly low if it is not a windy day. Radiation is probably also fairly low because I don't think paint on wood has a very high radiation coefficient.
If the top of the hive is open/has vents/has a quilt box you are going to have hot air rising out of the hive and sucking in cold air at the bottom. If the top of the hive is closed up you will not get as much heat loss this way. I am not sure how to do the math or where to look it up for this scenario.
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