Abstract: An elongated timber or lumber member (10) for an elongated, thermally insulating building construction element assembly (20) formed by first and second ones of said elongated timber or lumber member assembled along respective elongated adjoining surfaces (11) facing each other, said elongated timber or lumber member having a first fitting side (13) on a side located opposite to its elongated adjoining surface, said fitting side being spaced from said adjoining surface by timber or lumber of a respective thicknesses, and said fitting side being provided with a tongue or a groove (14A, 14B) to allow a plurality of the elongated, thermally insulating construction element assemblies to be juxtaposed to each other in alignment in a tongue and groove arrangement to form a thermally insulating building surface.