375 on single wall equates to about 750 F inside. That's okay (not too high), but not very low. You're pushing a decent amount of heat up there.
So a damper then is good, as it decreased the heat flow (both in magnitude of the volume of gas flowing, and the resulting temperature of that gas).
Whether it is a good system or not, that depends; if you choked down the fire too much you will get a lot of gunk in the flue.
I don't know if the Bullard has secondary combustion (tubes with holes in the top below a baffle) or not.
You need to see nice flame, either primary on the wood (if no baffle and no secondary air, as in the fisher), or secondary near the top of the firebox (if a baffle is present, and secondary air tubes). If you don't see that, you're smoking the neighborhood out.
So, I consider it good if you slow down the fire (while still getting sufficient heat out, with a slightly cooler stove!) AND you don't see smoke from the pipe outside AND you still heat your home sufficiently for your comfort.
"good" here is "increased efficiency". In the end (hypothetical nonsensical example for illustration) maybe you could increase efficiency by 150% if you went down to stove top temp of 150 F (of course nonsense, but

, but then you would not have enough heat for your home - so that's efficient but not good.
BTW measuring pipe temp on the outside of class A does not make sense. It's insulated.
(And don't drill a hole for a probe in class A either as it voids the warranty/UL listing = insurance agreement.)
So don't bother measuring the class A.
BTW, a burn time being good or not needs info on the volume of wood you got in there. What are the volumes of the fireboxes and did you stuff them full?