We systematically study the thermal and topological properties of X 2 Y 3 (X = As, Sb, Bi; Y = Se, Te) and the effects of pressure and temperature on their electronic properties using first-principles. We find that the external pressure-induced electronic topological transition occurs at about 5 GPa for Bi 2 Se 3 , and the type of band gap tends to become indirect with the increase of pressure. We also investigate the lattice expansion with temperature in quasi-harmonic approximation and further explore the effect of temperature on the volume, band gap, and volumetric thermal expansion coefficient of the studied selenides and tellurides. Finally, we calculate the evolution of the Wannier charge center of X 2 Y 3 to determine their topological invariants, and theoretically suggest that Bi 2 Se 3 changes from a topological to an ordinary insulator when the pressure decreases to -8 GPa; As 2 Se 3 is found to be an ordinary insulator, while all other four compounds are always strong topological insulators at any pressure or temperature.