Not in the slightest. In a properly designed stove, as opposed to a big vacant box, the hot gases are routed from the firebox, under the top from front to rear (giving off much heat also to internally exposed sides), then up and out at the rear. Or something similar. You most definitely want "more head trapped in the stove FIREBOX."
In my little Morso, it's possible to have the front of the top at 750 F and the smokepipe just above the stove at 300 F, then 220 F two feet further away. See the picture? As hot as possible for combustion efficiency, THEN work on dumping the heat. Organized schizophrenia?
It burns so completely that outside, downwind, you can barely pick up the scent.
Yep
My Comfort stove has 7 bricks across the top of the fire box that holds the gasses and heat in; I didn't know the difference till I replaced some cracked bricks and changed the door gasket how much heat I was losing