In this paper, we consider the problem of thermal stresses in an infinite plate with a pair of circular holes that are filled with elastic inclusions of another material. A steady-state temperature is induced by a pair of heat sources (positive and negative sources) placed on the x-axis. The analysis is developed by the Airy stress function in the case of generalized plane stress and by applying the bipolar coordinates. The method of perturbation is adopted for the determination of the unknown coefficients involved in the solution. Numerical calculations of the stress distributions along main parts of the infinite plate and the inclusions are worked out in some detail. The maximum stresses on the common boundaries are also calculated and compared with the available results.