Poly-quasicrystalline samples of an icosahedral Al-Cu-Fe alloy have been deformed in compression tests under constant-strain-rate conditions at temperatures ranging from room temperature up to 1020 K (m approximate to 1150 K, where T-m is the melting temperature). The activation volumes, which were measured by performing load relaxation experiments, were found to be small and reveal that two different thermally activated mechanisms belonging to two different temperature regimes, are responsible for plastic flow of icosahedral Al-Cu-Fe; the first mechanisms operates between 770 and 960 K, and the second at higher temperatures. The activation enthalpy Delta H has been determined for the low-temperature regime. Under the assumption that the entropy term arises mainly from the variation in the shear modulus with temperature, the activation Gibbs free energy Delta G has been deduced for the corresponding rate-controlling mechanism.