Here is a summary of a presentation given by Derek Mitchell a few years ago on the benefits (impacts) of insulating hives.

https://oxnatbees.wordpress.com/2015/01/25/warm-hives/

"Q. What’s the best insulated hive type?

A. The lecturers did some serious testing (2.3 million measurements!) on 8 types of hive (12 hives in total). For a 20 watt input – that’s equivalent to burning 20 teaspoons of honey a day – they saw the following temperature rises (there was a spread of results, this is my estimate of the centreline of the graphs they displayed) –

Natural tree cavity (6 inch thick walls) – 60 degrees C
Skep, sealed with cow dung – 22 C
Polystyrene hive (various types) – 22 C
Warré, walls just over 1 inch thick, 4 inch thick sawdust quilt on top – 16 C
Kenyan TBH with thick top bars, directly under a flat roof – 14 C
Wooden National – 7 C to 10 C"

He has also published a paper recently on the benefits of hive insulation and increased honey yields.
https://royalsocietypublishing.org/doi/full/10.1098/rsif.2018.0879

I live in the far north (Yukon) and I have been testing the use of polystyrene hives vs traditional wooden hives with just 2" insulation and the use of top entrances vs not using a top entrance over the last 5 years. I have had the best overwintering success without a top entrance and keeping my screened bottom board open. The fact that heat is kept in and not eject out via wall heat transfer or out a top entrance makes up for heat gain from the sun in a 24hr day. Bees will likely be more easily be able to maintain internal hive temps stable during typical spring diurnal temp swings.

https://www.northof60beekeeping.com/education/spring-2019-beescene (A few images of my setup, my climate). 

I ran 2 brood boxes x 9 frames in my polys this past winter and inserting a 1"x10" pine trimmed to a fame profile in the outside position in the hive box. This location was always filled with dead bees killed by excessive amounts of condensation dripping down the sides. It worked like a charm this year, no dead bees and 4 / 4 overwinters (best had with 16 frames of bees with at least 60lbs of stores left from ~100lbs, weakest had 6-8 frames and plenty of stores left). The next improvement will be to plane off 1/4 inch of these inserts, roughen up to inside surface to "encourage" the bees to propolise the surface. This is one area where poly hives do poorly on. The bees will not readily propolise the poly side and top walls.

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