depends on a lot of situations, direction of the wind outside being the main one. If the wind blows across your window it helps draw out the warm air allowing cooler air to convect in. If the wind blows at your window cold air blows in forcing warm air to leave, ie out of doors, up chimneys etc.
Usually with no wind, as dot.hawkes states the warm air leaves from the top the cold air enters from the bottom and you create a convection current.
OK. Lets say it's an average sitting room and the temperature inside the house is warm and the temperature outside is the house is cool. Open the window and what happens?