Monocrystalline alloy with a nominal composition of Cu-13.7% Al-4.2% Ni (wt.%) that shows reversible martensitic transformations (RMTs) was studied. The alloy, manufactured by the “Memory Crystals Group” in Russia, was subjected to thermo-cyclical treatment (TCT) under tension within a range that included critical RMT temperatures. A special device was developed to perform TCTs (up to 500 cycles) and three different loads were applied: 0.11, 0.26, and 0.53 MPa. X-ray diffraction analysis, optical microscopy, differential calorimetry, and Vickers microhardness were involved in the alloy’s characterization. Under TCTs, the alloy displayed complex structural transformation, revealing the sequence of RMT, β₁ ↔ R ↔ β′₁ + γ′₁; the involved phases were coherently precipitated but very sensitive to the experimental conditions. It was found that during TCTs (from 300 cycles) performed under optimum load (0.26 MPa), the processes of martensite reorientation, hardening, and stabilization of the structure were the most intensive thus leading to a reduction of RMT critical intervals and increased microhardness.