In this study, a model formulated at the ply scale was considered to describe the mechanical behaviour of an acrylic-thermoplastic-matrix and glass-fibre-reinforced laminated composite under monotonic tensile and fatigue loadings within a temperature range of −20 °C to +60 °C. This study showed that the temperature dependency of the composite transverse and off-axis mechanical behaviour could be determined concisely, by considering only the temperature dependency of the matrix initial elastic properties and keeping the parameters of the damage evolution laws constant. This is a relevant result for designing composite structures with a limited set of experimental data.