A temperature equation accounting for the compressibility as well as the elasticity of polymeric fluids is derived using the Massieu thermodynamic potential. The constitutive model is completed by adopting the Tait equation relating the thermodynamic pressure to the specific volume and the temperature. A Lagrangian numerical technique is used to study the behavior of the proposed model under different types of loading conditions against published models with an apparent degree of success. (C) 2015 Elsevier Ltd. All rights reserved.