>>"Yes, but my temperature probe reading of 58F (at the top center of the hive) when the outside air temperature is 5F (it's the same at 25F OAT) means that they ARE heating the hive.They ARE wasting heat.

I'm guessing that this measurement -- 58F (at the top center of the hive) --  is inside the outer part of the cluster?  That is roughly the ambient temperature at which bees form a cluster.

>> Would a smaller box or a better insulated box waste less heat?

Yes, however whether saving this heat or not is a good idea depends on whether it is time to raise brood or not and although bees like high humidity for brood rearing, the box must allow excess moisture and CO2 to escape.

Saving some of the heat can be a good plan even in dead of winter, but overdoing it or doing it in a way that causes condensation and ice formation above the cluster can be harmful.  If insulating and heating or crowding is overdone, the bees don't cluster much of the time and are too active during what should be their winter quiet period.  They consume too much feed and starve, hang out on sub-zero days or age too rapidly.  

I've see it all, since there has been quite a bit of experimentation by beekeepers I know, ranging from no insulation at all to bundling and crowding hives together to the extent that bees were forced to hang outside in clumps at zero degrees on still, sunny days.

>The cluster is breathing and exhaling CO2 and moisture.  This exhalation is at the heat level of the interior of the cluster and because heat rises, exits the cluster in a column up from the cluster.  This is the way air exchange takes place within the cluster so that air with abundant O2 replaces air that is abundant with CO2. The heating of the hive outside the cluster is incidental. They heat the air above the cluster, not the air beside the cluster (which is why colonies have starved to death with abundant honey stores on each side of the cluster) nor the air below the cluster.

Very true, but with good design, some of the heat escaping upwards can surround the cluster at least some of the time and allow the cluster to cover more comb, forestalling that starvation.  Bees can be seen in the cold of winter actually controlling the vents if the vents are placed appropriately and the conditions outside are calm.

Although the warmed air rising off the cluster contains C02 and H2O, it is not sufficiently saturated with either to be a problem unless ventilation is *very* restricted or unless there is a cold object (a heat sink) overhead to condense the moisture so that it either drips immediately or forms an ice cake that melts and soaks the bees on the first warm day.   (That is the main reason for overhead insulation - to prevent the lid from being a heat sink).

In winter, without brood, bees can do very nicely in free space as long as it is calm, however, when it is time to raise brood, they need to spread out more and and conserved heat can be beneficial provided that it is not accompanied by excess moisture that they cannot vent. 

If the hive is warm enough tight, close, insulated), active bees will ventilate to control their conditions and they can do it through very small holes.

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