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Numerical solution of conjugate heat transfer (CHT) problems in multi-region domains is a challenging issue in terms of efficiency and stability due to inherent coupling between governing equations in separate sub-domains. This paper aims at comparing two distinct strategies for coupling energy equations at interface of regions: partitioned and monolithic. While the former enforces strong coupling via iterative procedures, the latter suggests simultaneous solution of energy equation throughout all regions at once. More precisely, the primary objective of this study is to compare computational costs for three finite volume- based CHT solvers which share a same method for handling pressure-velocity coupling in the fluid, i.e. semi-implicit projection method, and are distinguished from the coupling strategy for energy equation at interface of interacting sub-domains. The first method applies simultaneous solution of energy equation across all regions while second and third ones use separate solver for each region with difference in handling iterative loops. The accuracy and convergence rate of three algorithms are assessed via transient solution of conjugate free convection in fluid and conduction in vertical wall. Finally, it is concluded that, in contrast to partitioned solver in OpenFOAM for CHT problems, employing a separate loop to enforce energy-energy coupling per iteration, can be much more beneficial in terms of computational costs. [ABSTRACT FROM AUTHOR]