The influence of the temperature and the heat treatment time on the Al64Cu23Fe13quasicrystal stability is studied in the present work. For this purpose the samples obtained by arc-furnace undergo different heat treatments varying the time and temperature of treatment. The structural characterization of the samples were carried out employing X-ray diffraction, and scanning electron microscopy, whereas the elemental composition was determined using energy dispersive x-ray spectroscopy. The results indicate that heat treatments are necessary to eliminate spurious phases which are always present after the synthesis of the samples. We also found that heat treatments of 800 ◦C by 48 hours or 700 ◦C by 168 hours are the most convenient ways to obtain samples with larger grain sizes (90 nm). Finally, the elemental analysis indicates a light deviation of the ideal composition due to the synth...