You can move either but cold air is easier to move as there are more molecules per cubic foot, once air (any gas or mixture of gases) warms the number of molecules per cubic foot is decreased because the distance between them increases due to their energy level (they fly apart). Moving the cold air down low puts it towards the stoves convection air intake. It then is more a matter of time (and heat loss between there and where the heat is needed). First you generate the heat then you move it all the while reducing your heat loss as much as possible. It is easy to bury a few tens of thousands of btus by not paying attention (such as attempting to heat an uninsulated basement or expecting the heat to still be there after running the air past a 100+ square feet of windows, I won't even mention gaps around them).