  We derive the incompressible Euler equations with heat convection with the
no-penetration boundary condition from the Boltzmann equation with the diffuse
boundary in the hydrodynamic limit for the scale of large Reynold number.
Inspired by the recent framework in [30], we consider the Navier-Stokes-Fourier
system with no-slip boundary conditions as an intermediary approximation and
develop a Hilbert-type expansion of the Boltzmann equation around the global
Maxwellian that allows the nontrivial heat transfer by convection in the limit.
To justify our expansion and the limit, a new direct estimate of the heat flux
and its derivatives in the Navier-Stokes-Fourier system is established adopting
a recent Green's function approach in the study of the inviscid limit.
