In this study, the numerical investigation of transient natural convection with respect to the effects of two-way fluid-structure interaction, is presented in a square enclosure containing a flexible baffle. The enclosure is filled with air of Prandtl number 0.71. Temperature is constant in both hot and cold vertical walls, while baffle and horizontal walls are adiabatic. Arbitrary Lagrangian-Eulerian (ALE) formulation is used to describe the fluid motion in the given model. Non-Dimensional fluid domain equations with relevant boundary conditions are discretized by the finite volume method (FVM), and PISO algorithm is used to solve the pressure-velocity coupling. Non-Dimensional equations of the baffle motion are solved by the finite element method (FEM) and Newton-Raphson iteration technique. Rayleigh number changes over the range of 10^3 to 10^6. Among the assessed cases in this study, 25 and 35 percentages of them indicate respectively, increase and decrease in the rate of heat transfer in compare with the enclosure containing a rigid baffle. Maximum and minimum values of Num,ss variation are respectively, 4.5 and -15.4 percent. In compare with the rigid baffle, about 90 percent of assessed cases indicate an increase in the time to reach the steady state situations, that it is not considered favorable.