My boxes have handles. Any issues with the air gap that'll result?
Actually with any insulation you are creating dead air space. The materials themselves are not the insulator, the air spaces the material creates is what makes it insulate. Big air gaps - > 1/2 inch are less effective. What is necessary is a way to prevent that air from moving and thus carrying the 'heat' away. The ideal air space is .25 inch or less.
Remember heat always moves to cold.
So, in a wet environment, I would use something like foam board as it will not soak up water and loose the air spaces in the material like the fiberglass or rockwool or cellulose types. But it has to be painted/covered to protect from UV,
A 1 inch airspace with an insulation is by far better than no insulation, so the handles should not really have an effect.
To use the foam board is easy, relatively inexpensive for a few hives, glues easily, cuts with a pocket knife, and if painted will last for many years.
So, the answer about the 'what if it gets too hot'....I don't have one. But with proper ventilation, there should not be a problem. The bees will control the air movement in the hive, what do they do in the summer when it gets too hot? Like I mentioned somewhere, I am seeing mine flying at the low 40 degree range on decent days. They did not do that before I made the slide over boxes....just take off the cover and slide them down in place...alll the way to the ground. They are just as much a wind barrier as insulation.