  We develop the first order gradient correction to the exchange-correlation
free energy of the homogeneous electron gas for use in finite temperature
density functional calculations. Based on this we propose and implement a
simple temperature dependent extension for functionals beyond the local density
approximation. These finite temperature functionals show improvement over zero
temperature functionals as compared to path integral Monte Carlo calculations
for deuterium and perform without computational cost increase compared to zero
temperature functionals and so should be used for finite temperature
calculations.
