Natural convection problem in a deformable outlet cavity is studied with lattice Boltzmann method. Heated size at left wall are set to two conditions: The whole wall (H) and the middle wall (0.5H). The right wall is open to external environment. The upper and lower boundaries are adiabatic and their right end can be moved up and down to adjust size of the right outlet. Effects of Rayleigh number (10⁴ ≤ Ra ≤ 10⁶), the right exit size (1.0H ≤ L ≤ 2.0H), the left wall heating size (L_h=0.5H or L_h=H) on streamlines, isothermal lines, local Nusselt numbers and average Nusselt numbers are investigated. It shows that heat transfer in the cavity increases with the increase of Rayleigh number, which manifests as size of elliptical quasi-stationary region in the cavity increases and is closer to the upper and lower adiabatic boundaries. Thickness of thermal stratification is gradually reduced and average Nusselt number is increased. However, increase of the right outlet has a different degree of influence on heat transfer effect in the cavity. As the heating size is in the middle of the left wall surface, size of the right side opening does not significantly affect the heat exchange. In addition, at the left wall heating size of 0.5H it shows a higher average heat transfer efficiency. An empirical prediction of functional relation between average Nusselt number and control parameters is proposed. The fitting function satisfies practice and design in projects.