We present a partition of unity-enriched element-free Galerkin method for thermoelastic twodimensional crack problems. Therefore, the displacement field is enriched by the step enrichment. In the vicinity of the crack tip, the asymptotic branch enrichment functions commonly used in linear elastic fracture mechanics are employed. The same enrichment strategy is employed for the temperature field. Level set functions are used in order to model the crack surface. The accuracy of the method is demonstrated for three examples, one involves the crack propagation due to temperature and mixed traction-temperature loading conditions with complex curved crack paths.