"Hot Dog!"

My 22 month old beagle is often "hot" to the touch, especially her mouth. The inside of her mouth turns bright red and she pants fairly hard with her tongue out. This happens during cool days and when shes inactive or sleeping.
   
I have mentioned this a couple of times to two of her vets, (I've known, used and trust for many years) both of whom didn't seemed concerned.
   
Should I push the issue harder or is this normal for this breed?
   
This is my second beagle, didn't have this with the first one.