Wood Heaters, page-187

Yes we have this type flue design. They are a real conundrum. They only draw air in when the heater is hot enough and if the house is sealed enough to be more resistance than drawing the air down the flue. Of course drawing hot air down hill requires more energy than cold air would. (referring to house air leaks here)
Once the fire cools down hot air from the room bleeds out via the flue venting.
Im guessing they are designed to prevent people asphyxiating themselves given the modern trend of sealing the house to aid insulation.
If for some reason it was cold and you couldn't light the fire the ideally you would need to seal the room side flue vents to minimise heat leakage. We never touch ours.