The fixing device includes at least one holding element (14) through which a pipe passes, and a thermal insulating device (10) to insulate the pipe thermally from the floor. The insulating device is in the form of a strip layer, which has a number of annular zones (16) enclosing annular slits (18,20). The holding element is assembled in such a manner as to compress the insulating material within an enclosed zone against the floor. There may be several concentric slits in one zone. The holding element may consist of a pressure plate (22) to press the insulation to the floor.