If a mouse can get its head through a hole I think it can get the rest of its body through 5mm is the right gage for a mouse cage.I agree too high a temperature is more harmfull.My shed has heating inside radiators and thermostaiclly controlled fan heater which is not pointed at any of the mice for draughts I keep it at a constant 60 F, 18 c about the fan heater was on quite alot in that cold spell but I wasnt bothered as long as the mice were ok, importantly good ventilaltion is a must too in hot summers if we get any 
.Before the shed roof was put on it was lined with foil sheeting if you can get hold of some of this do it is great for insulating the roof its used to line metal storage containers.And my shed is raised 2 ft off the ground to keep vermin away from underneath .Keeping your mice in the house is fine maybe not in a bedroom where someone is sleeping noisy wheels and mice scratting keeps you awake lol.
.Before the shed roof was put on it was lined with foil sheeting if you can get hold of some of this do it is great for insulating the roof its used to line metal storage containers.And my shed is raised 2 ft off the ground to keep vermin away from underneath .Keeping your mice in the house is fine maybe not in a bedroom where someone is sleeping noisy wheels and mice scratting keeps you awake lol.
