In this paper, our previous ghost-cell compressible immersed boundary method (Luo et al., 2016) is further implemented to solve heat transfer problems in flows with complex solid geometries. Arbitrary 2D immersed boundaries are presented by many micro line segments. Each line segment is identified by two vertices. An extension to 3D situation is straightforward, in which arbitrary surfaces can be divided into many triangular surface elements. Two different interpolation schemes for the mirror points, namely inverse distance weighting and bilinear interpolations, are compared. An accurate capture of the secondary vortex street far behind an elliptical cylinder indicates a successful combination of current IB method with the fluid solver. Then, forced convective flow over an inclined non-circle cylinder is used to further validate present method. Finally, Mach > 0.3 cases are studied to demonstrate the essentiality of taking compressibility into consideration in high-speed thermal flow problems. (C) 2016 Elsevier Ltd. All rights reserved.