The need to accurately predict heat transfer in aircraft anti-icing systems or in turbomachinery cooling passages is a current topic of Computational Fluid Dynamics (CFD). In both applications, the flow structure is highly complex and three-dimensional. The traditional use of correlations might be useful in describing the average heat transfer behavior, but not the localized effects. Accurate heat transfer predictions are required to design efficient complex cooling or heating schemes and only a full 3D Navier-Stokes code, coupled with a solid conduction code, is the sole alternative. Conjugate Heat Transfer (CHT) is the commonly used term to identify such coupling of convection and conduction across one or several fluid-solid interfaces.  The CHT approach proposed in this thesis solves both the fluid and solid thermal fields simultaneously, in a fully-implicit manner using the infrastructure of a 3D Navier-Stokes flow solver, FENSAP. The algorithm supports 3D structured, unstructured, and hybrid meshes, with mismatched node connectivity and with non-uniform grid densities between fluid and solid domains at CHT interfaces.  The heat transfer validation is assessed for both laminar and turbulent flows against relevant open literature data. The CHT validation is assessed with three cases: a blunt flat plate flow, a fully-developed pipe flow, and the complex piccolo tube system flow in a 3D nacelle lip. The results show that the proposed method can be used as a reliable and cost-effective tool for the analysis and design of thermal anti-icing devices, and can easily be extended to cooled gas turbine components, such as: blades, vanes, shrouds, and disks.