  We consider a flow of heat conducting fluid inside a moving domain whose
shape in time is prescribed. The flow in this case is governed by the
Navier-Stokes-Fourier system consisting of equation of continuity, momentum
balance, entropy balance and energy equality. The velocity is supposed to
fulfill the full-slip boundary condition and we assume that the fluid is
thermally isolated. In the presented article we show the existence of a
variational solution.
