The mechanical characteristics of a rubber part depend on the temperature in a nontrivial way. While pure rubber materials stiffen, many filler reinforced compounds show decreasing moduli with rising temperature. Further, every deformation of rubber induces a change in temperature, which manifests in cyclic self-heating. In order to cover the observed effects precisely, a thermomechanically coupled problem has to be solved. The presented material model employs the concept of representative directions, as described by Freund & Ihlemann (2010). The concept extension for the sake of thermomechanical simulations is discussed. A comprehensive mechanical model is enhanced in order to account for the found thermal effects within the laws of thermodynamics. A parameter adaption for the developed coupled material model is presented for a natural rubber filled with carbon black. In a range from -20 to 80°C, the quasi-static behavior is described in decent quality with one set of material parameters. An FE-simulation shows the capability of predicting self-heating in a transient and fully coupled scheme covering the internal heat sources according to the thermo-elastic effect, entropy-elasticity and the modeled dissipative effects.