If your boxies is gaping, that's a sign of respiratory problems. Warm him up and see if he continues to gap. If it looks like he is having trouble breathing, take him to a vet. He may need anti-biotics. Chances are, he was probably not feeling well before hand. You should not hibernate any animals that are ill as the stress would likely cause them to go downhill and probably perish.
If your animal is captive bred or even if it's not, it's your choice to hibernate or not to hibernate. I typically only hibernate mature adults because it affects their breeding behavior to not have a seasonal cycle. Babies and yearlings or even younger subadults, if you don't have to hibernate them, then don't.
Let me know if you have further questions.
Paul