By 5 or 6 weeks Lola will probably be looking to give the little guy away!!
The moms do lose interest in their pups around then (the weaning period). By then it shouldn't matter what temperature the room is that you have them in... you can move them to the family room then.
I keep my house so cold (and I have 3 litters of pups at the moment)... my husband recently asked me if I was thinking about hanging meat around the house!!! ( I guess he was cold...)
I just have a blanket over the side of the xpen nearest the vent in the sunroom.
Good luck!!