The paper deals with the calculations of heat capacity of quasicrystalline decagonal Al69Co21Ni10 and icosahedral Al63Cu25Fe12 quasicrystalline phases of Al–Co–Ni and Al–Cu–Fe alloys, respectively. According to the Gruneisen law, heat capacity is an energy characteristic, which reflects the phases’ resistance to failure. For calculations of the heat capacity, structure of quasicrystalline phases is considered in the model representation of anisotropic crystals. As a result, it is found that the heat capacity of quasicrystalline phases at high temperatures is the excessive one, i.e. it exceeds the Dulong-Petit value. Therefore, quasicrystalline phases at high temperatures are more stable, than the crystalline phase. For the decagonal quasicrystalline phase, heat capacity is more than 3R in the temperature range of ~480–1500 К, and for the icosahedral quasicrystalline phase – in the temperature range of ~380–1120 К. It follows that decagonal phases remain stable at high temperatures at which the icosahedral phases are destroyed.