Constitutive equations are derived for the viscoelastic response of rubbery polymers at finite strains. A polymer is thought of as a network of long chains connected to temporary junctions. At random times, chains detach from the junctions, which is treated as transition from their active state to the dangling state. A dangling chain captures a new junction in the vicinity of its free end at a random instant and returns to its active state. Breakage and reformation of long chains are modeled as thermo-mechanically activated processes. Stress-strain relations for a rubbery polymer are developed using the laws of thermodynamics. Adjustable parameters in the model are found by fitting observations in uniaxial tensile tests for a carbon black filled rubber at various temperatures. Fair agreement is demonstrated between experimental data and results of numerical simulation.