The influence of neutron irradiation on the temperature kinetics of thermoelastic martensitic transformation in a Cu-Al(13.4%)-Ni(5%) alloy single crystal is investigated by measuring the electrical resistivity directly under irradiation of the sample in a nuclear reactor channel. It is revealed that, after irradiation of the crystal in a martensitic or two-phase state, the temperature of the phase transition upon healing becomes 25-30 K higher than that prior to irradiation. This shift in the transition temperature is observed only upon the first heating, and the kinetics of martensitic transformation is restored in subsequent thermocycles. The shift in the transformation temperatures after irradiation increases with an increase in the fluence. The experimental results are explained by a disturbance of coherence at the interfaces in the irradiated crystals.