Believe me, not only will the fire be just fine, but you could probably get away with a much smaller barrel--30, maybe smaller.
Many many years ago, I had a friend in Montana who had a hot tub in the woods. He would fill it from a nearby stream and heat it with a nifty little submersible woodstove. It was about as big as a 5 gal can, had a 4" chimney, a 2" air tube, a water-tight front door, and the whole thing slid up and down on a track. It was as simple as stacking a fire in the box, lighting it, shutting the door and lowering it into the tub. He couldn't even put a 'full' load in it or it would overheat the old-school 4-person cedar hot tub he was using it in. He said it was army surplus and that were smaller and larger versions in existence. In fact, I was at the local surplus store last month and saw a similar unit, but it was $500!