A pair-roll system consisting of a rubber-covered roll and a driving metallic roll is often used in industrial machinery such as printing machines and paper-making machines. In this paper, a new finite element formulation of thermo-viscoelasticity is proposed to determine the stress and temperature distributions in the rubber layer in a steady-state rolling contact problem. In this approach, the time derivatives are converted to the higher order spatial ones by means of the Galilean transformation, resulting in no direct time integration. Heat Generation due to viscous energy dissipation and the strain-rate dependence of viscoelastic properties of the rubber are taken into account. To demonstrate the accuracy of the proposed method and its applicability to existing machines, numerical calculations for thermo-viscoelastic responses of a pair-roll system have been conducted, and the results have been compared favorably well with experimental ones.