The basic constitutive equations for a mixture are given by Green and Naghdi . In the present paper, we follow , and we obtain the thermoelastic equations for a mixture of an elastic solid and a fluid. We observe that the thermoelastic equations of a mixture and the Lame's equations of the thermoelasticity are formally the same. Throughout this paper, we find a more generalized form of Betti's reciprocal theorem and Maysel's formula for a mixture. Finally, a solution of a spherical thermal inclusion of radius a in an infinite mixture is obtained by using generalized Maysel's formula and by direct integration of the governing differential equations.