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A thermodynamical system can be described by the field equations that are governed by the balance equations and the appropriate constitutive equations. For polymer melts or adhesives under thermal loading nonlinear constitutive equations are necessary. The development of nonlinear constitutive relations compatible with the thermodynamical principles is presented according to ordinary and extended irreversible thermodynamics. The necessary material constants in these constitutive equations are obtained by exploiting an energy based method. This method is demonstrated and applied for an epoxy (non-cured) adhesive measured in a cone-plate rheometer. The balance and constitutive equations result in a set of nonlinear and coupled field equations that is solved with analytical and numerical techniques for various problems.