Moving buns into insulated shed from cold room

I know I've been asking a few questions along these lines recently, but if you were to move buns from an indoor room, which is pretty cold and the house has no central heating into a properly insulated outside shed, would it matter when temperature wise? Does anyone know how many degrees warmer an insulated shed is to the outside temperature? The buns fur is often cold to touch in their room, and they have the room window open so I'm wondering if there would be any worries moving between the two? I'm going to try and get hold of a thermometer to take the temp of their room and compare. The shed I'm considering is tongue and groove if that makes any difference?

Thanks