The paper presents a full-field strain analysis of the appearance/disappearance of twinned martensite in a Cu-Al-Ni single crystal subjected to thermal cycles. Localized Spectrum Analysis (LSA) was employed to process images of a checkerboard pattern preprinted on the sample's surface, enabling us to obtain strain maps with a suitable trade-off between strain resolution (2×10-4) and spatial resolution (0.26 mm). During the cooling of the initially austenitic sample, habit plane variants (HPVs) were identified from the in-plane components of their mean right strain tensor. The match between measured data and theoretical expectations enabled us to measure the stretch parameters associated with the cubic-to-orthorhombic transformation occurring in the material. Various deformation mechanisms were revealed by an analysis in the strain space. In particular, the process of martensite appearance during cooling appeared to be based on the coordinated activation of HPVs pairs whose strain levels globally compensate each other. Elastic strain gradients were also evidenced, highlighting the need for additional deformation to achieve kinematic compatibility at microstructure interfaces. Lastly, several thermal cycles were applied to the previously-trained sample, enabling us to quantify the level of spatio-temporal repeatability of the phase transformation.