A skinny barrel will heat faster and cool faster. The rate you are guessing at ( 30 to 50 ) per hour. That's every 1 to 2 minutes. Your skinny barrel is going to heat up,but you will be fine for a while. That ( every 2 minutes) is a pretty slow fire rate. The walking of the bullets would be my last concern ( only considering what you are shooting at ). My concern is the damage you could do to your barrel by heating it up to much. ( got 2 rifles
). No sense in damaging a barrel over a dog.