  In this paper, we study a nonlinear interaction problem between a
thermoelastic shell and a heat-conducting fluid. The shell is governed by
linear thermoelasticity equations and encompasses a time-dependent domain which
is filled with a fluid governed by the full Navier-Stokes-Fourier system. The
fluid and the shell are fully coupled, giving rise to a novel nonlinear moving
boundary fluid-structure interaction problem involving heat exchange. The
existence of a weak solution is obtained by combining three approximation
techniques -- decoupling, penalization and domain extension. This approximation
scheme allows us to use the methods already developed for fluids on moving
domains, thus drastically simplifying the analysis at hand.
