We describe a supersonic molecular-beam source that can be heated to over 2300 K. Our design employs a commercially available tungsten tube which is resistively heated by passage of current along its length between two water-cooled copper clamps. The clamps are supported so as to minimize bending stresses on the tube while allowing for thermal expansion. Gas is supplied to the tube at one end using an o-ring connection and emerges from an orifice drilled about halfway along the length. The other end of the tube is welded closed. Temperature is measured by a thermocouple spot-welded adjacent to the orifice. The entire tube is surrounded by two tantalum heat shields which are split lengthwise for convenient assembly. These have large holes aligned with the beam axis. We present details of the design, assembly, and characterization of this source.