The present study submits a mixed finite element model to solve atransient thermoelastic contact of non-conformal deformable bodies.The model is concerned with the coupled quasistatic class ofthermoelasticity in which the inertia term is discarded. Attention iscentered on homogeneous and isotropic materials whose thermal andelastic properties do not depend on the temperature.The nature of the problem depends strongly on the direction of heatflow and the value of distortivity of the two bodies. This model can beused for the case of heat flows into the material with larger distortivity.The solution’ procedure consists of two simultaneous variationalmodels. The first one concerns with the transient heat transfer problembetween the two contacting bodies considering the conventional thermalboundary conditions at the contact interface. The direct integrationmethod is used to discrete the time domain of that model. The secondmodel is an inequality-constrained model, which concerns with thefrictionless thermoelastic contact problem. The mathematicalprogramming method is used to handle that model. Throughout thecontact interface both thermal and mechanical boundary conditions areinforced by using the convex programming procedure. Such procedure isapplied incrementally on the time domain of the problem.Several problems, with different geometries, boundary and loadingconditions are analyzed and examined by using the developed model. Thetemperature distribution and the contact status, including contact area andcontact pressure are predicted. Also, the effect of different distortivitiesupon the contact status is detected.The obtained results demonstrate clearly the efficient applicabilityof the developed model to handle the transient thermoelastic frictionlesscontact problems.