Abstract: A spacer plate for use in making a hollow floor has a plurality of truncated cone-shaped spacer elements extending from one side of the plate, and distributed in a row wise and column wise arrangement, for supporting the spacer plate from an underfloor, and also formed in the spacer plate are grooves formed in the same side of the plate as the spacer elements for holding a pipe conducting a heating or cooling medium, with the grooves surrounding at least a half of the circumference of the pipe to securely hold the pipe in place on the plate, so that the heating or cooling medium conducted through the pipe can come into heat exchange relationship not only with an upper floor laid on top of the spacer plate but also with air conducted through space existing between the spacer plate and the underfloor.