Based on detailed 2D numerical radiation hydrodynamics (RHD) calculations of time-dependent compressible convection, we have studied the dynamics and thermal structure of the convective surface layers of stars in the range of effective temperatures and gravities between 4500 K ≤ Teff ≤ 7100 K and 2.54 ≤ log g ≤ 4.74. Although our hydrodynamical models describe only the shallow, strongly superadiabatic layers at the top of the convective stellar envelope, they provide information about the value of the entropy s∗ of the deeper, adiabatically stratified regions. E.g. in the solar case the helioseismically measured entropy jump is predicted within 9% of its actual value.