When a viscoelastic material is applied by a sinusoidal excitation of which frequency is relatively high and amplitude large, we can recognize a phenomenon that the temperature of the material increases, while the apparent dynamic stiffnesses decrease. It is considered that the phenomenon is caused by the temperature dependence of the dynamin properties of the material and internal heat generetion for mechanical damping. There are, however, few papers on the vibration analysis of the viscoelastic materials taking into consideration the temperature dependence of the dynamic properties and internal heat generation. In this paper, a new analysis method is presented in order to examine the vibrating viscoelastic material on the steady-state response, and then the method applyed to two dimensional problem of viscoelastic material undergoing a sinusoidal displacement, under the fixed thermal boundary condition. Analytical results were reduced to the mean temperature, the total heat generation rate and the apparent dynamic stiffnesses, and the relationships between each quantites are found. As a result of consideration for the relationships, new equation for mean temperature was derived, moreover it is shown that apparent dynamic stiffnesses are also determined by the solution of the equation.