Abstract: A heat insulating roof structure for an industrial building, in the form of an inter-purlin system comprising spaced parallel purlins (10, 10A or 35, 35A or 45, 45A) having their base webs (14 or 41 or 50, 51) sheathed by a heat insulating sleeve (16, 17 or 53, 54 or 56, 57), thereby to provide lateral platforms on opposite sides of the purlin for the support of cross members (29 or 70) which form trays to support a layer of heat insulating material (31). In one form of embodiment the cross members are inverted tee bars (29), thereby forming open rectangularly framed trays for supporting the insulating layer. In another form of embodiment the cross members are closed tray bases (70) especially suitable for a vapor sealed system. In all embodiments the insulating sleeve assembly (16, 17 or 53, 54 or 56, 57) serve to minimize or avoid the creation of a cold bridge between the warm building interior and the cold space above the insulating layer (31).