First-principles calculations of the structural, electronic, optical and thermal properties of chalcopyrite CuXTe₂ (X[Formula: see text]=[Formula: see text]Al, Ga, In) have been performed within density functional theory using the full-potential linearized augmented plane wave (FP-LAPW) method, by employing for the exchange and correlation potential the approximations WC-GGA and mBJ-GGA. The effect of X cations replacement on the structural, electronic band structure, density of states and optical properties were highlighted and explained. Our results are in good agreement with the previous theoretical and experimental data. As far as we know, for the first time we find the effects of temperature and pressure on thermal parameters of CuAlTe₂ and CuGaTe₂ compounds. Thermal properties are very useful for optimizing crystal growth, and predict photovoltaic applications on extreme thermodynamic conditions.