  We present a numerical study of turbulence and dynamo action in stratified
shearing boxes with zero magnetic flux. We assume that the fluid obeys the
perfect gas law and has finite (constant) thermal diffusivity. We choose
radiative boundary conditions at the vertical boundaries in which the heat flux
is propor- tional to the fourth power of the temperature. We compare the
results with the corresponding cases in which fixed temperature boundary
conditions are applied. The most notable result is that the formation of a
fully convective state in which the density is nearly constant as a function of
height and the heat is transported to the upper and lower boundaries by
overturning motions is robust and persists even in cases with radiative
boundary conditions. Interestingly, in the convective regime, although the
diffusive transport is negligible the mean stratification does not relax to an
adiabatic state.
