Abstract: An air inflated structure, the outer shell walls of which have a surface geometry consisting of one or more concave sections. Heat flow from or into the enclosed volume is drastically curtailed by thin plastic films, which are secured to the outer boundaries of the concave surface sections, and are joined to the shell wall at locations within the boundaries of its curved surface section by direct attachment or via flexible anchor tie strips.The surface area of each film is less than that of the surface geometry encompassed within the boundary to which it is secured, whereby in its inflated state, the outer shell wall extends the films in a taut fashion across its curved surface geometries to define a thin, uniform and dimensionally stable insulating air space between the shell wall and the plastic films. Additional sets of plastic films, spaced approximately parallel, may be utilized to further curtail the said heat flow.