We explore the dependence of {T_eff}'s and colors of stellar models on the treatment of over-adiabatic convection, both in the atmosphere and in the interior. We compute main sequence, turnoff, and subgiant models for low metallicity stars (Z=2 10-4) using as boundary conditions two new sets of model atmospheres by the Wien group (Kupka \cite{kup96}; Smalley & Kupka \cite{sma97}; Heiter et al. \cite{hei01}). In these models convection is treated either in the Mixing Length Theory (MLT) or in the Full Spectrum of Turbulence (FST) formulation. We check the dependence of the {T_eff} location of the HR diagram both on the optical depth tau at which the atmospheric boundary conditions are fixed, and on the convective model adopted in the atmosphere and interior. Obviously, full selfconsistency of the result is obtained only if the treatment of convection is the same in the outer layers and in the interior. We show that it is not appropriate to use MLT convection in the atmosphere and FST in the interior; if we wish to test the effect of changing the l/H_p in the MLT, the atmospheric integration must be limited to tau =1. We construct isochrones for ages of 10 Gyr and greater, and transform the theoretical {T_eff} and gravity values to the Johnson B and V magnitudes. The two sets of model atmospheres give small differences (up to ~ 0.03 mag) for the B-V color, a result of the different temperature stratification in the model atmosphere with FST convection treatment compared to that one based on MLT. The FST boundary conditions provide relative locations of turnoff and giant branch which differ from the MLT solutions, and are in better agreement with the HR diagram morphology of the Globular Cluster M 92.