Your rad was holed and basicaly leaking then.....

The header tank was only overflowing because of an airlock caused by water leaking out of the cooling system at low temperature.

The terms you used were not clear as you usually notice a puddle under the car rather than air in the cooling system. Air is displaced by the water and can only return back into the system if there is a coolant leak allowing air to return to where there was once water.

Are you sure you don't have an underlying problem like a head gasket failure?