A supplemental window apparatus includes a foot and a first constraint element attached to the foot. The foot and the first constraint element are configured to be detachably coupled to a window pane of an existing window through a mating constraint element. A spacer is coupled to the foot and is configured to extend at least partially in a direction perpendicular to the window pane when installed on the existing window. A substantially non porous sheet is coupled to the spacer and has a sheet area substantially similar to a window pane area defined by the interior surfaces of the first window element holding the window pane. The spacer substantially defines a gap between the sheet and the window pane when installed on the existing window. The foot extends outward from the spacer toward the interior surfaces of the first window element.