Thermal errors of the transform lens are characterized by surface deformation, position shift and extra aberration. A beam propagation model is further proposed by the ray trace method. Beam properties such as intensity distribution, beam quality, and spectrum have been analyzed. Results show that the surface deformation degrades obviously beam quality and broadens the spectrum of the combined beam. The position shift affects the intensity peak, and also degrades beam quality. Side lobes of the combined beam become increasingly obvious due to the growing extra aberration. A movable platform and a spatial filter are suggested to optimize combined beams.
