There are two volumetric heat sources in a liquid-metal sliding electrical contact for a homopolar device : Joulean heating and viscous dissipation. The Joulean heating is created by the presence of electric currents; the viscous dissipation results from the motion of the liquid metal and is enhanced by magnetohydrodynamic (MHD) effects. In a homopolar device, the liquid metal is confined to a small gap between the perimeter of a rotating disk and the surrounding static surface. The maximum temperature achieved within the liquid metal is significantly larger for an MHD flow than for an ordinary hydrodynamic flow, a flow in the absence of a magnetic field. Information concerning the temperature distribution within the liquid metal and solid parts of a homopolar device will result in the design of efficient and operational sliding electrical contacts.