Modular thermal truss plates carry heat in multiple directions. Framing around an array of flat heat pipes provides mechanical and thermal connections to other truss plates, and a base, such as a satellite, thereby supporting thermally active equipment. Walls sandwich banks of flat heat pipes and may bond to a honey comb, metal core conducting heat between multiple walls. Each bank of flat heat pipes passes heat best in one direction, and may be formed of corrugated copper sheets spaced apart by a metal mesh, such as an expanded metal or screen, also stamped or otherwise formed into a corrugated configuration. Joining methods (e.g., brazing, soldering, etc.) increase stiffness, pressure containment, and strength, by binding the two layers of metal sheet to one another.