If the fan is on high with an already cool box it may reduce the box temps enough to reduce or kill the secondary burn. Most stoves do not have thermostatically controlled fan speeds, just a snap disk for on/off. The user has to adjust the speed.
KaptJaq
There is only secondary burn when the gases are burning off, which here is usually the first 1/3 to 1/2 stage of the burn in my Summit. A cool box is not going to have secondary burn going on, as it is well past that stage of burn.
My fan stays on high full time, except when I am reloading or not burning. I get same secondary burn as I do without the blower on(during power outages).
Secondary burn is about firebox/baffle feed air temps and the volatile gases that are igniting, causing such secondary burn, and I have yet to see my blower reduce internal fire box temps to come anywhere near the point of killing secondary burn. Does it cool the insert down? I am sure it does, but not enough to affect the secondaries, nor have I seen any drastic reduction in burn time.
Loading every 12 hours with the 2600 sf home heated just fine with fan blowing on high.
The blower should be used to regulate/distribute heat as needed for ones comfort level.
I myself would much rather have the warmth I want, then try to squeeze an hour or two extra heat time out at the expense of a cooler home.
There are X amount of BTU's out out from a load. I see distribution of this heat in a more house wide manor and temps for my comfort, much more efficient then taking less heat off the stove to be distributed around the home.
Every set up and home is different, so what works for me, may not work for others &Vise Versa.
To state a general blanket statement for all instances just does not hold water.