Two upper collinear cracks are placed parallel to a lower crack in an infinite orthotropic plane under uniform heat flux perpendicular to the cracks. The surfaces of the cracks are assumed to be thermally insulated. The mixed boundary value conditions with respect to the temperature field and those with respect to the stress field are reduced to dual integral equations using the Fourier transform technique. In order to satisfy the boundary conditions outside the cracks, the differences in temperature and displacement at each crack surface are expanded in a series of functions that are zero outside the cracks. The unknown coefficients in each series are evaluated using the Schmidt method. The stress intensity factors are then calculated numerically for selected crack configurations.