Ed Southwick did a lot of work on heat in hives, honey stores consumption, hive energetics.  Bottom line, bees don't necessarily die of cold - he took them to minus 80 C.  The survival  was a matter of a sufficiently large cluster and enough food. 

The take home of his papers and  my conversations with  him - there is a sweet spot where a reasonably large cluster can maintain appropriate cluster heat at a minimal energetic cost.  Warm winters, bees stay too active and consume more food.  Extreme cold, and the consumption rate also goes up.

There  were some large studies done in Minnesota many years ago about heating hives.  

But, just  as with overwintering sheds, you  don't want to warm them too much.  


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