  We study the motion of a compressible heat-conducting fluid in three
dimensions interacting with a non-linear flexible shell. The fluid is described
by the full Navier--Stokes--Fourier system. The shell constitutes an unknown
part of the boundary of the physical domain of the fluid and is changing in
time. The solid is described as an elastic non-linear shell of Koiter type; in
particular it possesses a non-convex elastic energy. Its deformation is
modelled by a (non-linear) elastic Koiter shell. We show the existence of a
weak solution to the corresponding system of PDEs which exists until the moving
boundary approaches a self-intersection or the non-linear elastic energy of the
shell degenerates. It is achieved by compactness results (in highest order
spaces) for the solid-deformation and fluid-density. Our solutions comply with
the first and second law of thermodynamics: the total energy is preserved and
the entropy balance is understood as a variational inequality.
