Go ahead and close the door, Just don't fill the stove up with pine and then turn the draft down every time you use the stove, in doing so you will just build up creasote in the flue. It is OK to put in a few logs and turn down the stove at bedtime. You will get the hang of it, the smoke out of your flue should not be black, or heavy dark grey but should be blueish grey to clear that you can see through. Also get a flue thermometer so that you can keep the fire in the proper heat range.