This work involves a numerical investigation on free convection heat transfer occurred by a hot cylinder immersed in a square duct cooled from one side under different temperatures. The right vertical wall of the enclosure has been subjected with various cold temperature (T_r), whereas the remaining enclosure walls have been insulated. Finite volume approach with ANSYS–FLUENT has been used to solve the governing formulation. Simulations have been done for a large ranges of Rayleigh number (10³≤ Ra ≤10⁷) and right wall temperature (0≤T_r ≤0.75). The results displayed that Nusselt number (Nu) is enhanced with rising in Ra and decreasing in T_r. The fluid temperature is decreased with rising in Ra and it is increased with rising in T_r. The value of Nu is decreased with rising in T_r, where the maximum reduction in Nu is about 32% for the dimensionless right wall temperature T_r=0.75 as compared to those obtained with T_r=0. The maximum enhancement range for the average Nu is found between 50% and 100% for low Ra and between 20% and 30 % for high Ra. The variations of local Nu, streamlines and isotherms displayed that Ra has an extremely actions on the flow characteristics and temperature fields.