The current numerical study aims to evaluate the thermal performance of natural convection flow in an asymmetrically heated two-dimensional vertical channel with conducting sidewalls for the variation in modified Rayleigh number and thermal conductivity ratio. The study is performed within a range of Rayleigh numbers (Ra_L) between 10⁴ to 10⁶ and with air (Pr 0.72) as the working fluid. Results indicate that the consideration of the conducting wall significantly affects the velocity and thermal distribution inside the channel. The intensity and occurrence of the recirculating flow increases, the level of thermal saturation decreases, the relative mass flow rate decreases and the average Nusselt number based on the channel air-gap calculated on the heated wall increases with the increase in thermal conductivity ratio. This increase in the average Nusselt number is found to be marginal at modified Rayleigh number higher than 10⁴ but significant below 10³ where its distribution increasingly deviates from the usual composite correlation with the increase in thermal conductivity ratio. This is driven by the heat transfer through the conducting wall for a relatively narrow channel and an increase of the average Nusselt number on conducting wall with the increase in thermal conductivity ratio. This study with conducting walls of finite thickness presents a more realistic analysis of the thermal performance than that with an adiabatic wall condition usually considered in many literatures.