A rotating toroid is considered as a target for the production of pions by intense high energy proton beams for a neutrino factory. The toroid rotates in vacuum and the power is radiated to the water-cooled walls of the vacuum chamber. It is shown that steady powers of over 100 MW can be dissipated by thermal radiation at temperatures of ∼2500 K, using a suitable refractory material such as tantalum or tungsten. Under pulsed beam conditions, the thermal stresses induced in the toroid will reduce the power capabilities. ©2000 American Institute of Physics.