Actually, warm air, which is less dense and therefore lighter than cold air will tend to rise above cold air as a result of air pressure. Heat transfer will occur in all directions, because heat moves from areas of high temperature to areas of low temperature, including through the floor of a heated space to an unheated basement.
If your home is built over a crawlspace or unheated basement, you can lose a lot of heat downward through the floors. Insulation will help reduce that loss and also make your floors feel warmer in the winter.