This paper presents a monolithic approach to the thermal fluid-structure interaction (FSI) with nonconforming interfaces. The thermal viscous flow is governed by the Boussinesq approximation and the incompressible Navier-Stokes equations. The motion of the fluid domain is accounted for by an arbitrary Lagrangian-Eulerian (ALE) strategy. A pseudo-solid formulation is used to manage the deformation of the fluid domain. The structure is described by the geometrically nonlinear thermoelastic dynamics. An efficient data transfer strategy based on the Gauss points is proposed to guarantee the equilibrium of the stresses and heat along the interface. The resulting strongly coupled set of nonlinear equations for the fluid, structure, and heat is solved by a monolithic solution procedure. A numerical example is presented to demonstrate the robustness and efficiency of the methodology.