If you read the package insert on the SMB boots or the Classic Equine boots (or honestly just about any boot), it says that you should never have the boots on for more than 2 hours because they do trap heat around the legs.
I'm not even convinced that the Air Boots breathe enough to not have to take them off either. I've never seen them in person, but looking at photos, the material that is in contact with the legs is NOT vented on the inside.
Polo wraps (in my opinion) will breathe better than a sport boot because they aren't made of neoprene. Do they breathe well enough to not have to take them off? I don't know about that.
To keep things simple, just don't put on your horse's leg protection until you are ready to run. Then it minimizes the time the boots are on.
∞•*˚ Βгįťţαňγ ˚*•∞
It is not enough to know how to ride; one must know how to fall.