The results of thermoactivation analysis of the temperature dependence of hardness for icosahedral quasicrystals (QC) of the Al—Cu—Fe system obtained as a coating, massive compact and ingot are presented. QC as well as covalent crystals at room temperature are brittle without signs of macroplastic deformation at standard methods of mechanical testing and only the method of local indenter loading makes it possible to deform QC to significant degrees of deformation without fracture. In the studied temperature range 77—1073 K, the HV(T) hardness dependences have the same character, despite the state in which the QC was obtained. The HV(T) dependence consists from two sections: an athermal low-temperature section (77—600 K) and a section (>600 K) where the hardness decreases sharply with increasing temperature. The presence of a low-temperature athermal section on the HV(T) dependence is explained by the phase transition of the QC to a more plastic approximant phase. Phase transition of this type can be associated with a high density of phason defects, which are formed during the deformation of the QC that leads to violations of the atomic structure. Based on the experimental data of the temperature dependences of the Vickers hardness (HV) obtained by the authors and the literature data, the values of the activation energy of the dislocation motion U and the activation volume V of a number of icosahedral quasicrystals were calculated. It is shown that the value of U 0,97—1,83 eV, and V is (65—132)∙10-24cm3. Previously, the method of thermoactivation analysis of tempera¬ture dependence of a flow stress was applied to materials with different crystal structures (BCC, FCC metals, covalent crystals, refractory compounds, intermetallics, high entropy alloys). In comparison with crystalline materials, the values of thermal activation parameters of the deformation process for QC are close to refractory compounds (carbides, borides) which have a covalent component in the interatomic bond. Keywords: quasicrystals, activation energy of dislocation motion, activation volume, hardness, temperature.