Fluid-solid interaction phenomenon study is necessary for the analysis of several engineering systems such as structures and vessels that interact with wind and blood flow, respectively. In this study, the interactions between buoyancy-driven airflow and elastic baffle(s) inside a square enclosure were modeled numerically. While the two sidewalls of the enclosure were insulated, the lower and upper walls were kept at hot and cold temperatures, respectively. The heat transfer rate through the hot wall by calculating the Nusselt number and von Mises stress at the baffles’ root for various configurations of baffle(s) was considered. The domain was modeled in ANSYS Workbench, and the k-ε model was employed to solve the turbulent convective flow (Ra > 107). A two-way algorithm along with the finite element method was employed to simultaneously solve the equations governing the fluid flow and the solid phase. The dynamic mesh method was employed to account for the change in the location of the fluid domain at a new time step. The results show the elastic baffle, in comparison to solid baffle, intensifies the heat transfer rate by 15%. The results also indicate that the Nusselt number in the single-baffle case is higher than in double-baffle cases. The fact that the amount of von Mises is a function of the baffles’ configuration is another point obtained from the results. It was found that the von Mises stress at the baffles’ root represents more unsteady fluctuations in the asymmetric case, while it approaches a constant value in the symmetric case.