Abstract: This paper presents a solution strategy for the combined identification of constitutive parameters of viscoelasticity and temperature field via quasi-static displacements. A numerical model, facilitating to sensitivity analysis, is developed for the solution of direct viscoelasticity problems with temperature field. The corresponding inverse problem is converted into a problem of non-linear programming with multi-constrains of inequality. It can be further converted into an optimization with a single differentiable constraint by exploiting a maximum entropy based on aggregate function method. A technique of multiplier penalty function is used in search of the optimal solution. Numerical results are presented and the effects of both time-independent and time-dependent noise data on the results are discussed.