If we're discussing scientifics, we need the number of bees in the cluster, the necessary cluster temp (well documented), amount of food (honey and fondant) consumed and the fact that polystyrene insulates against cold but also does the same for heat.
Heat is the killer here and hence the travelling screens used in hive use in v hot climates.
Peter S
"The other thing is that they do not have a roof space for fondant - hence the eke. "
Take the 'conservatory out of the full width rapid feeder and use that for fondant. Very efficient!
Ok I have looked to this and come with the calcs as with all scientifics there are some assumptions.
1) endothermic output 17w National comsuming the equivalent of 12.5kg of sugar in 150 days we get a endothermic(deliberate heating activity ) out put of 17w.
2) ectothermic output 5 w (heat put when they are lollling around) from 1w per Kg of bees we get 5w.
3) target temperature 34c (based on scientific papers reporting a bee in cluster brooding etc.
4) if the temp is below target the bees will commence endothermic heating. At target ectothermic. above target cooling or venting required by bee or beek
5) other hives will produce heat is proportion to the volume with respect the volume of a national hive.
6) the hive loses heat equally on all sides (not strictly true but we will assume this for the basis of this exercise)
7) brood box only considered
Thus we can calcluate for hive sizes and materials the range of external temperatures that the bees can choose to heat the whole hive space.
in particular we can see the temp at which cooling (vents evaporation) has to commence
for a 50mm polystyrene national temp range is from -0.2C to +23.9C
50mm polyurethane -17.3 to +18.9
25 mm polystyrene +14.3 to +28.21
25mm oak +29.8c to +32.8c
19mm oak +30.7 to +33.0
940mm(37") dia 240mm (9.5") thick walled hollow oak tree trunk -0.23c to +23.9c
So if you have a 50mm poly hive you might think to open the vents when the temp is above 23C
for 14x12 we get temps 2 -5 c different