Thermoelectric (TE) materials exhibiting energy converting and storing capabilities connected with an electrode are increasingly applied in engineering sciences. The contact interfaces of the TE devices are prone to gradual degradation or even failure under thermal shock loading. The investigation of the dynamic contact problem of the TE materials loaded by an electrode is significant for designing reliable TE devices. The transient frictionless contact model of the TE materials with a finite thickness indented by a rigid flat punch is proposed and investigated in this paper. The considered thermal-mechanical coupling problem is converted into the corresponding singular integral equations by the Laplace transform and the Fourier transform techniques, which are solved numerically by a collocation method. Then, the numerical inverse Laplace transform is employed to obtain the time-domain solutions. The time-dependent and thickness-dependent surface normal energy flux and surface normal contact stress, which are significant for the transient contact behavior, are computed and analyzed. The magnitudes of the transient normal energy flux and normal contact stress differ from that in the steady-state. Specifically, the normal contact stress in the transient state is higher than that in the steady-state.