  (abridged) The calculation of the thermal stratification in the
superadiabatic layers of stellar models with convective envelopes is a long
standing problem of stellar astrophysics, and has a major impact on predicted
observational properties like radius and effective temperature. The Mixing
Length Theory, almost universally used to model the superadiabatic convective
layers, contains effectively one free parameter to be calibrated --alpha(ml)--
whose value controls the resulting effective temperature. Here we present the
first self-consistent stellar evolution models calculated by employing the
atmospheric temperature stratification, Rosseland opacities, and calibrated
variable alpha(ml) (dependent on effective temperature and surface gravity)
from a large suite of three-dimensional radiation hydrodynamics simulations of
stellar convective envelopes and atmospheres for solar stellar composition
(Trampedach et al. 2013). From our calculations (with the same composition of
the radiation hydrodynamics simulations), we find that the effective
temperatures of models with the hydro-calibrated variable alpha(ml) display
only minor differences, by at most ~30-50 K, compared to models calculated at
constant solar alpha(ml). The depth of the convective regions is essentially
the same in both cases. We have also analyzed the role played by the
hydro-calibrated T(tau) relationships in determining the evolution of the model
effective temperatures, when compared to alternative T(tau) relationships often
used in stellar model computations. The choice of the T(tau) can have a larger
impact than the use of a variable alpha(ml) compared to a constant solar value.
We found that the solar semi-empirical T(tau) by Vernazza et al. (1981)
provides stellar model effective temperatures that agree quite well with the
results with the hydro-calibrated relationships.
