Using the single generator bracket formalism of non-equilibrium thermodynamics, we build a thermodynamically consistent constitutive equation of the differential type for linear entangled polymers. The starting point of our developments is the MGI rheological model proposed recently by Marrucci et al. [Rheol. Acta 40 (2) (2001) 98], which can be viewed as a modification of the classical Doi-Edwards reptation theory that includes convective constraint release and a modified strain measure. The proposed constitutive equation has an additional parameter which governs the dissipative part of the model. The MGI model is recovered as a particular case, but with a stress-conformation relationship which contains an additional term suggested by non-equilibrium thermodynamics. Predictions of the proposed model in steady and transient shear flows are shown to be in qualitative agreement with experimental observations.