Most (but not all) CDHs have motherboards and controllers that allow one to fine-tune their air/fuel ratios. My Warmtoo XMZ-D2 5kW heaters came out of the box with too low fan speed and pump Hz setting when on Low, so I increased them slightly to prevent a slight rhythmic pulsing from the exhaust with puffs of smoke: I increased the pump's minimum Hz from 1.4 to 1.5, and increased the minimum fan speed from 1450 to 1750 RPM. It now burns absolutely cleanly on Low with no smoke at all, even at 4000 feet ASL; what's more important is that it now always maintains greater than 120C burner temperature on Low to prevent incomplete combustion and soot buildup. After running all night there is now no soot at all inside the exhaust pipe, and there is no measurable CO on my CO alarm/meter. If your CDH's burner temperature drops below 120C it will accumulate soot inside the burn chamber. I did not change the upper pump Hz or fan speed, just the lower ones. Most "experts" say that to adjust for higher elevations one should reduce the pump Hz, but I strongly disagree: if there's less air, isn't it logical to instead increase air (by increasing fan speed)? This is exactly why turbocharged engines perform better than NA engines at higher elevations: their fuel is certainly not turned down! One person said that CDHs' fuel should be reduced by 4% per 1000 feet, but if you did that at 12,500 feet there would be a 50% fuel reduction which is plainly insufficient to maintain any combustion, let alone clean complete soot-free combustion.
I don't think that the Afterburner controller will save an appreciable quantity of fuel by shutting the heater completely off when the room temperature is reached. If using a standard pump that moves 0.022 ml of fuel per stroke, in one hour at a pump rate of (hypothetically) 1.5 Hz it will have moved only 118.8 ml (only about 4 fl.oz in USA-speak), a completely inconsequential amount of fuel! More to the point, if the glow pin is heating up every time the heater restarts, this will appreciably shorten its life and consume much more power from the battery.
John