We propose both monolithic and partitioned approach to solve conjugate heat transfer in an immersed boundary framework for complex geometries. The present framework is based on the staggered/non-staggered finite volume framework for incompressible flows which is extended to handle conjugate heat transfer. The key difference in the monolithic framework is that only a single hybrid momentum equation for normal momentum and single hybrid energy equation for temperature are solved simultaneously for both fluid and solid domains. However, in partitioned approach the energy equation is solved in each sub domain and temperature of both domains are coupled using suitable boundary conditions. The equations are discretized using a second-order accurate spatial and temporal scheme, that uses three point backward differencing for time discretisation and high-resolution schemes for convective discretisation, while central differencing is adopted for the viscous terms. The resulting discretized non-linear system of equations are solved using the Newton-Krylov approach. The momentum field at the cell centroids is then reconstructed using a defect-correction algorithm. The energy conservation equation is discretized similar to the collocated framework, with a second-order convection scheme for the convective terms and implicit Euler time stepping. These equations are linearized by considering the velocity field at the latest available time step, and the resulting linear system of equations are solved using SAAMG preconditioned GMRES solver using the LiS library. The effect of immersed solids are accounted for in the governing equation using a solid fraction approach. The investigations are be carried out for conjugate heat transfer with a backward-facing flow at different ratios of solid to fluid thermal diffusivities. Studies show that both monolithic and partitioned approaches can successfully simulate conjugate heat transfer with a backward-facing flow although the former shows a faster convergence to steady state solution. © 2018 by the authors of the abstracts.