Fireplaces, Heating Stoves, Flues and Chimneys - a theoretical chimney question

I know that hot air drives the updraft but if the fire is not lit is there a natural movemebt of air up the flue? As long as the room is not airtight will there be a nutural updraft -and will it increase as the air outside above the chimney becomes windier?

Actually it isn't the hot air that drives it up, but the difference in temperatures that causes it to move. Cold air replaces the hot air at the bottom and the hot air naturally rises. There is natural movement in the chimney due to things like wind. If constructed correctly, although your house may be "airtight", the fireplace has fresh air intakes (code) for ignition of combustibles. If you have doors on the fireplace, closing them will allow only the fresh air to be drawn in and moved up the chimney, leaving your room air alone. Closing the flue will keep movement to a minimum as well.