I'd be a little concerned about this... it's a temperature shock if it's 40 inside and 7 outside, as they're going in and out. They don't really need the heat, it mostly just makes us as humans feel better, but a big enough temperature drop can sicken or kill a bird.My hubby was worried about his girls so he ended up putting in a ceramic barrel heater at night we close the door and it keeps it at 40 deg f and the temp outside this morning was 7 f .
You can put leaves in the run however keep in mind that leaves will start breaking down and can get slimy. Ideally you'd mix them with other litter, such as chunky aged wood chips, which would help provide drainage and aeration to the leaf mix as it breaks down.
I've already tossed in several inches of leaves into my run and will be adding more soon. I also have some 18 bags more in storage for use in the run and for composting throughout next year, so I do make sure to put my leaves to good use!