Conjugate heat transfer (CHT) considers the simultaneous solution of heat transfer in adjacent solid and fluid domains. It is a classical coupled problem that can be solved in a monolithic or partitioned fashion. This work implements the partitioned approach in the existing fluid-structure interaction (FSI) framework CoCoNuT, with the aim to extend it to problems with solid-liquid phase change and interface motion in future work. Instead of exchanging displacement and forces on the interface between both solvers, temperature and heat flux are exchanged to achieve a thermal equilibrium on the interface. If temperature and heat flux are exchanged unmodified between the subproblems in each coupling iteration of a time step, this coupling strategy mirrors Gauss-Seidel iterations for FSI problems. This approach has proven to be stable for only a limited range of Biot numbers [1]. However, the FSI framework allows the use of more efficient and robust coupling strategies for CHT problems, such as quasi-Newton methods [2]. Furthermore, integrating CHT into the FSI solver extends its applicability to problems involving thermal fluid-structure interaction. The coupling framework is evaluated and validated for both conduction-only and convection-driven cases. The test geometry consists of a rectangular domain divided in half, with solid and fluid zones and a straight interface between them. The performance and accuracy of Gauss-Seidel iterations are compared to coupling methods employing virtual heat transfer coefficients and quasi-Newton methods through a numerical stability analysis. [1] T. Verstraete and S. Scholl. Stability analysis of partitioned methods for predicting conjugate heat transfer. International Journal of Heat and Mass Transfer, 101:852–869, 2016. [2] N. Delaissé, T. Demeester, R. Haelterman and J. Degroote. Quasi-Newton methods for partitioned simulation of fluid-structure interaction reviewed in the generalized Broyden framework, Arch. Comput. Method Eng., 30: 3271-3300, 2023.