the benefited claims tend to be better egg production, less feed, better health. if you don't track inputs and outputs then there is no way to conclude one way or the other about what venefits there may be. some of us feel that it helps others don't and pretty much none of us have enough information for conclusion at this point.
If I have the same temps, in my uninsulated coop, as somebody else, with an insulated coop, what differences do you expect to see? We have the SAME temperatures in the coops, with the same outside temps. But for some reason, if one coop has insulation, they are going to have better productivity out of their chickens? That doesn't make any sense at all.
I don't think that's a fair comparison since you're not accomodating in differences in dimension, number of birds, etcetc.
Not really necessary to look at egg production unless someone wants to argue the insulation itself, and not the temp increase due to the insulation, has a positive effect on production.
All you'd really need is two coops of identical sizes and (adequate) venting, one with insulation and one without, located in similar conditions next to each other. Then you fill them with the same number of birds with more or less the same qualities and compare temperatures.
If someone needs a summer product...