Thermal fluid-structure interaction (TFSI) arises in many critical applications, where the coupling between fluid flow, structural deformation, and heat transfer governs system behavior. Accurately capturing such multiphysics interactions remains challenging, particularly when dealing with complex geometries, large structural displacements, and moving interfaces. Immersed boundary (IB) methods provide a versatile and efficient framework for simulating TFSI problems by decoupling the fluid and solid meshes and enforcing interfacial conditions through momentum and thermal forcing terms. This review presents a comprehensive survey of recent advances in IB methods tailored for TFSI. We classify the methods based on their interface treatment into two main categories: direct forcing approaches, which use smoothed forcing to approximate boundary conditions, and reconstruction-based methods, which impose sharp interface conditions via interpolation. Applications to both rigid and elastic structures are discussed, including cases involving forced and natural convection, particle-laden flows, and bioheat transfer in vascularized tissues. Coupling strategies, including monolithic and partitioned frameworks, are reviewed with a focus on their stability and computational efficiency. Finally, open challenges and future directions are outlined, highlighting the need for robust coupling algorithms, adaptive time integration, and interface-aware discretizations to address the complexities of TFSI.