Don't let them run or at least not for very long when it's on the warmer side.
It's amazing how quickly over heating can happen.
As I've said I did with Dakota, a cool damp cloth applied are the ears and head, and a cooler area. Even standing in front of the freezer with the door open is good.Waving it for a quick cool. I used this for asthma attacks as well.
I know we should not get a chin wet, but if it's life or death do what you must. Just remember not to soak them just a cool damp cloth.
I find mine chins stress less if I have them up, so I used a real cool piece of cotton sheet, to help keep my body heat from getting to Dakota, and not cuddling him just holding him.