Wow! This was an impressive thread to read. I have to say that I have learned something, adding heat to the cluster in the spring to help with the build up. Now I have to share what I know from my father.
My father read an article written by a researcher during the communist regime, when beekeeping was strongly encouraged in my country (Romania), about the benefits of heating the hives during winter. The researcher used regular foundation wire zigzagged on a bottom board, totaling 10W at 12V, painted (because he used galvanized wire, and it still rusts). He also used a microcontroller with a temperature sensor placed in the middle of the hive towards the back, outside of the cluster (middle on the vertical and lateral, towards the back longitudinal). The microcontroller will turn on the heater by a relay, only when the temperature was below +6C. This prevented too much activity from the bees and less food used to keep warm in too cold days or nights. Basically, he tried to emulate the conditions of an indoor wintering, when the bees stay at a constant temperature. The researcher weighed the hives before and after, he set up different temperatures in different hives, no heater in others, did all sorts of variations to see what works best. So it wasn't just guess work, it was research, and he published the results. So, my father built similar heaters, used a thermostat, and he wintered hives that would have died otherwise. He had no winter mortality for many years until the varroa became a big problem (got resistant to the treatments). He also reduces the space inside the hive to the frames the bees completely cover, so they have less space to heat up, he uses only one entrance, situated at 2/3 from the bottom (a bit higher than the Hoffman line) and he heavily insulates the inner cover to eliminate condensation.
So I have decided this winter to experiment a bit with his setup and add a little more to it, since technology has advanced since that research was done. I have ordered parts for 5 bottom heaters: 5 temperature sensors, 5 relay boards (unfortunately the relay boards were returned to sender by customs - stupid bleep happens in Canada). I have plenty of Arduino compatible microcontrollers, since my other hobby is robotics. I have also bought 4 humidity/temperature sensors and another one that works to lower temperatures (to keep track of the outside values). I want to use these last sensors placed on top of the hive, in the hole I have in the inner cover, below the insulation, to measure the amount of the humidity and temperature variance in the hives with different entrances. All the data will be logged by date and hour into a micro SD card by the microcontroller so I can read it later and plot a graph and see what setup works best for my location. I don't have all the parts yet to actually place the setup in the hives yet, but I will probably start with the humidity sensors and add the heaters later when the temp sensors and the relay modules will come in. I will take pictures and post the data collected, so there is no guess involved. I will also weigh the hives at the time I will start the experiment and weigh them again at the end, to see the food consumption. If you have suggestions of what I should also record, or other things I should try, please let me know. I may be able to add them to the experiment. Thanks.