In the present paper, we consider the problem of thermal stresses in an infinite plate with an infinite row of circular holes which are filled with elastic inclusions of another material. The steady state of temperature is induced by the infinite row of pairs of heat sources (positive and negative sources) periodically placed on either side of the infinite row of inclusions. The analysis is developed by the Airy's stress function in the generalized plane stress. In the construction of temperature and stress functions, periodical harmonic functions are utilized as the fundamental stress function. The successive approximation is adopted for the numerical determination of the unknown coefficients involved in the solution. Moreover, numerical calculations about the stress distributions along main parts of the infinite plate and the inclusions are worked out in some detail, in order to clarify the effects of an infinite row of circular inclusions.