Being a ground gripper and not a swinger myself I appreciate the problem!
If you make the linner with buttons or a two way zip you can let the heat out. I have found that using the same method as the old pattern 58 linner works the best. Make the linner entry so it matches the zip in your bag, side or top/central etc, ect. Then add ties to the corners to hold it in at the bottom and top, then four ties along each side of the zip.
You can also add a hood to the linner try fot the kind you see on a duffle coat, a basic bag, its easier to get off and on than a draw string type.
This way its easy to take out and wash, you can make a cotton one for summer use so you dont dirty up your bag.
My central heating boiler went bang during the cold snap, it was so cold at night I used my bag, while everyone else complained of the cold, I had a problem of being to warm! 5 days with no heat, hot water is very interesting. I got the art of a bucket bath down to a fine art.
Sandsnakes
In summary, go for ties