The immersed boundary method (IBM) was used for three-dimensional numerical simulations, and the results for natural convection in a rectangular channel with an inner hot circular cylinder are presented. This simulation used Rayleigh numbers spanning 3 orders of magnitude, from $1\xd7103$ to $1\xd7106$. The Prandtl number considered in this study was 0.7. We investigated the effects of the inner cylinder's radius on the thermal convection and heat transfer in the space between the cylinder and rectangular channel. A map of the thermal and flow regimes is presented as a function of the cylinder's radius and the Rayleigh number.