  For orbital-free {\it ab initio} molecular dynamics, especially on systems in
extreme thermodynamic conditions, we provide the first pseudo-potential-adapted
generalized gradient approximation (GGA) functional for the non-interacting
free energy. This is achieved by systematic finite-temperature extension of our
recent LKT ground state non-interacting kinetic energy GGA functional (Phys.
Rev. B \textbf{98}, 041111(R) (2018)). We test the performance of the new
functional first via static lattice calculations on crystalline aluminum and
silicon. Then we compare deuterium equation of state results against both
path-integral Monte Carlo and conventional (orbital-dependent) Kohn-Sham
results. The new functional, denoted LKTF, outperforms the previous best
semi-local free energy functional, VT84F (Phys.\ Rev.\ B \textbf{88}, 161108(R)
(2013)), and provides modestly faster simulations. We also discuss subtleties
of identification of kinetic and entropic contributions to non-interacting
free-energy functionals obtained by extension from ground state orbital-free
kinetic energy functionals.
