Etiger,
I'll give it a try.
Let's say my chimney is 20 feet tall and my chimney/liner is not insulated. Cold air is denser and heavier than warm, so I will have a good volume of cold exterior air in my chase/chimney. This will keep my uninsulated liner quite a bit cooler than it would be if lined. This cold air is heavy, and will want to stay down in the chimney. If I am burning, the liner will get warm, and that will warm some of the air in the chimney/chase as well. so some of that air will rise and be displaced by cold exterior air. So, I'll have two drafts going, one in the liner, and one in the chase/chimney. The greater the differential between the temp in the chase/chimney and the flue/liner, the greater the draft in the area around (outside) the liner/flue will be. The greater that draft is, the more rapidly the cold air outside will replace the slightly warmed air in the chimney. And the more rapidly it is replaced, the less time it has to warm, and the more cold air you are pulling down into your structure. And the more cold air there is available to cool the insert/flue.
If the flue/insert is insulated, there is much less heat exchange between the flue/insert and the air outside it, within the chimney. So that air does not heat as quickly, and will be sluggish and sit around the liner/flue more. It will very gradually heat, and to a lower temperature. That heated air will rise, but more slowly, and it will be denser because cooler, so there will be less differential between it and the outside air, so the draft will be much lower (I'm talking the draft AROUND the flue/liner. So your flue/liner loses less heat to the outdoors and stays warmer, and the area around the flue/liner stays warmer, so your home should also be a bit warmer.
Now, let suppose that with this 20 foot chimney and an uninsulated flue/liner, I am able to shut the air down to just open a fraction, and I get a good secondary or cat burn. I have a certain size opening letting air into the stove.The air is being pulled into the stove by the draft created by the air exiting up the chimney at a given speed. The cold air around my flue/liner is cooling the inside air in the flue/liner somewhat, and doing so more the colder it is out, because not only is the outside air colder to begin with, but also the differential between the inside and outside is greater, creating a greater draft around the flue and moving more cold particles by it each moment, and each particle passing along it is exchanging heat with it and cooling it a bit. So the possible draft inside my liner is kept somewhat lower by the cooling of the exhaust gases as they rise. The cooler they are, the less excited the particles in the air are, and the slower the air moves. The slower it moves up, the slower air is pulled into the stove. The slower air moves into my firebox, the less the volume of air that enters it in a given time., The less air that enters and leaves, the less oxygen in the stove in a given time,. The less oxygen in the stove the less fuel for burning the wood. The less fuel for burning the wood, the more unburned gases escape up the flue. The less oxygen inthe firebox, the cooler the burn will be, and the more primary as opposed to secondary burning will take place. More potential heat will be lost up your chimney, less heat over the length of the burn will warm your home. The slower the air moves up your insert, the more time it is in contact with the cooling exterior chimney air, and the more it cools and slows down, and the more likely your are to have creosote formation.
Now, if you line that flue/insert, and shut the air down on your 20 foot liner to the same setting, you are able to keep most of the warmth in the flue from meeting the colder chimney air. This keeps the chimney air from heating so fast, so it stays stiller longer, is displaced less frequently, moves along the flue taking heat away from the flue more slowly, keeps that area warmer and thus the home somewhat warmer than with an uninsulated liner. It also greatly reduces the amount the outside air is able to cool your flue, so it lets you maintain a higher stack temperature, which means that at the same setting (air opening), you will have hotter air leaving the flue. The hotter air is more excited and moves faster. It pulls more air into the firebox much more quickly though the same size opening. The air moving much more quickly though the same size opening brings with its increased volume more oxygen. There is now plenty of oxygen as fuel to let all the gases burn. The gases burn really hot, and the depleted air and burn byproducts are hot and move rapidly out of the firebox and up the flue, as new air/oxygen is introduced.
Now you are able to close the air down further, maybe half way or the remaining possible amount, or maybe all of it, depending on your set up. Hypothetically, lets say you close it enough so that the opening is small enough to let the same volume of air into the firebox that you let in at the larger opening/slower draft. So now you don't have a richer amount of fuel, you have the same amount. But you do have it moving through the firebox faster, so it burns the volatile gases that are high in the firebox really well, but it doesn't sit very long on the logs, so it doesn't have time to burn them as much. So, while you get a really efficient burn, you also get a longer burn.
That's what I think happens, more or less.