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Solutions are obtained for the interaction of two ellipsoidal inclusions in an elastic isotropic matrix with polynomial external athermal and temperature fields. Perfect mechanical and temperature contact is assumed at the phase interface. A solution to the problem is constructed. When the perturbations in the temperature field and stresses in the matrix owing to one inclusion are re-expanded in a Taylor series about the center of the second inclusion, and vice versa, and a finite number of expansion terms is retained, one obtains a finite system of linear algebraic equations in the unknown constants. The effect of a force free boundary of the half space on the stressed state of a material with a triaxial ellipsoidal inhomogeneity (inclusion) is investigated for uniform heating. Here it was assumed that the elastic properties of the inclusions and matrix are the same, but the coefficients of thermal expansion of the phases differ. Studies are made of the way the stress perturbations in the matrix increase and the of the deviation from a uniform stressed state inside an inclusion as it approaches the force free boundary.