It can be enough to set off a smoke alarm. That's why I always recommend connecting a couple pieces of pipe on the stove outside and cure the paint outdoors. Depending on the paint, some are worse than others.
If you were trying to exhaust smoke from the house with a mechanical fan, that will bring the smoke right in as well. When you understand the principal of the hot gasses rising up the flue to make the "vacuum" in the stove to allow the PUSH of atmospheric air pressure in, you'll realize every fan that exhausts air out of the house depressurizes the home. You no longer have enough atmospheric air pressure inside the house to push into the stove intakes. So a kitchen range exhaust fan, bathroom fan, clothes dryer, even oil or gas burners that exhaust to the outside pull air from the home. If no window is cracked near the stove (for atmospheric air pressure to get to the stove intakes) and the house is tight, the chimney becomes the only air INTAKE. So the rising gasses are competing with mechanical blowers. These are very minute pressures less than your breath. In rare cases a stairway near the stove can allow heat to rise so rapidly, the heat moving away from stove becomes a lower pressure area than the inside of a cool chimney and the intakes become exhaust. This is called stack effect, only in certain configurations with a poor drafting chimney should this happen.
I start with paper or cardboard and kindling on top. Open flue damper and spin draft caps open 2 or 3 turns. Light and close doors. When you hear a roar going up pipe, I slowly close the flue damper until the roar stops. This allows air pressure pushing in the intakes to give the fire as much oxygen as it needs. If you slow the roar with air intakes, you starve the fire of oxygen and this is not the time you want to do that. Open damper in a few minutes before opening door to add larger pieces of wood. Close doors and it should come back to a dull roar and you should be able to close down to about 2 turns. If the roar continues, tilt damper enough to slow it down. You're trying to prevent most of the heat from rushing up the stack so the heat is used to get the larger pieces going. As the stove comes up to temp you should be able to open damper and close intakes down to about a turn. If you notice a lot of smoke coming out of chimney, give it more air. (when you noticed smoke leakage, you should have opened flue damper and opened air intakes to kick up the fire instead of closing it down cooling the chimney further) I usually have an established fire in about 10 minutes. Fuel has a lot to do with it and you'll learn which makes good kindling. Place wood in so the flames have to change direction to get up through the wood pieces. When starting keep air space between wood pieces as much as possible.
If you have the fire screen, you can also use it to start fires very easily. It will give the fire all the air it can get and you can close doors as soon as fire is established. This is a trick to starting with damp kindling which is never good, but can help in an emergency situation when that is all you have. This is another reason I prefer single door Bear Series stoves. Logs put in lengthwise get air rushing down between them and the air rushing in sounds like an oil burner. They start easier than your wide firebox getting air across the wood. It's all about oxygen mixing with flammable gasses as they are expelled from the heated wood. Flames are the ignited gasses coming out of the wood.
After a couple fires you'll learn the tricks to make it take right off. It will act differently with a bed of ash as well. When removing ash always leave about an inch to burn on. If you keep the stove going, you won't be starting with paper and cardboard. Simply remove a little ash in the morning from the front where it burns down overnight. Rake some ash ahead with coals. Lay kindling on the glowing coals and open damper as well as intakes a few turns. It should take right off and be able to add larger wood within minutes. Again, you should be back to 1 turn open as it comes up to temp.
The thermometer is calibrated for single wall pipe. Without an IR thermometer checking pipe and chimney flue at the top, you can only guess the temperature drop to the top from where you put the thermometer. With an established fire, try it a foot above stove on pipe (heat from stove will affect it as well this low) then raise it and note how much it cools. Check pipe temp where it dumps into insulated chimney at box. Figure 300* at this location is going to be close to 600* flue gas temp, so depending on chimney size and material cooling to the top is a guess. 250* internal is the temp to stay above all the way up. This is why an insulated chimney performs best, staying hot inside with less heat needed to be lost up the flue. You will know by how much creosote forms. Check it frequently and if it stays clean, close damper very slightly and monitor temps and how much creosote forms. It will only form creosote when smoke is present, so in the coaling stage temps will be down doing no harm. You can even close the damper with a pile of coals to prolong the burn, but until you get used to it, err on the side of leaving it open more than closed.
Stove top temperature doesn't mean much and varies from lower and upper cooking surfaces. As a general rule, with a baffle in the stove I adjust baffle for twice the stove top temp as the single wall pipe a foot above damper. That gives you about 550 to 600* stove top at 300* pipe temp. (fine for an insulated chimney with short vertical pipe run) Move the thermometer around with a gloved hand and record temps to get an idea what stove temps are compared to pipe temps. An IR thermometer is instant and worth the investment. Same as a moisture meter. I highly recommend both.