It is given an algorithm for constructing of the first order gradient theory of thermoelasticity (strain-gradient theory). The model is a generalization of the applied model of interfacial layer, and it is obtained by involving the hypothesis Duhamel-Neumann. The mathematical formulation of the model reduces to a boundary value problem with resolving operator of high order as for all models of gradient elasticity. Physical relations of the model take in account the higher gradients of the temperature field than in the classical theory. The paper presents the test calculations for the layered composite structures, based on which we demonstrate the features of the model associated with possible accounting of local concentration of thermal stresses in the area of boundaries of the medium.