A nonstationary coupled problem is considered for thermoelasticity of a plane layer of semi-transparent gray, absorbing, radiating, and isotropically scattering elastic material. One of the boundary layers is heated by an external flow of radiation energy and convection at constant intensity. To solve the problem numerically, a vector modification of the Thomas method is used. The thermal and strain fields in the half-transparent material have been determined. Their interaction manifests itself by temperature pulsations and quantitative variation in the values of thermoelastic stresses of an object. A wide range of optic parameters are considered for the medium and the conditions of heat transfer with the environment.