Abstract Single crystals of 82.5 wt.%Cu–13.5 wt.%Al–4 wt.%Ni which present the β′(18R) thermally induced martensitic transformation after quenching from 1120 K, were submitted to mechanical tests in the compression mode at different temperatures. The studied temperatures were chosen between M f and A f in order to have the sample completely in β′ martensitic phase or in a mixture of β′ and β parent phase before applying stress. Under compression the γ′ (2H) martensite is induced in both cases. From the σ– ε curves, the critical stresses ( σ c) have been determined. The σ c– T diagram shows a linear decrease of the stress (in absolute value) when increasing the temperature, contrary to the well known increase of absolute value of critical stress with the temperature when the γ′ martensite is induced from the austenitic phase. The d σ c/d T value obtained from the σ– ε curves has been compared with that calculated from the Clausius–Clapeyron equation by combining the entropy change Δ S β′−γ′, calculated from calorimetric runs for the β↔β′ and β↔γ′ transformations, and the experimental strain data. In what concerns strain values, it has to be considered that when applying stress on the sample in β′ martensite two processes occur: the deformation of the thermally induced martensite in the sense of the applied stress (variant reorientation) and the formation of the γ′ martensitic phase. A set of experiments done at constant temperature up to different strain levels followed by calorimetric runs allowed us to separate both strain components and to obtain reasonably good agreement between the theoretical and experimental d σ c/d T values.