  Using the methodology of conditional-probability density functional theory,
and several mild assumptions, we calculate the temperature-dependence of the
Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA). This
numerically-defined thermal GGA reduces to the local approximation in the
uniform limit and PBE at zero temperature, and can be fit reasonably accurately
(within 8%) assuming the temperature-dependent enhancement is independent of
the gradient. This locally thermal PBE satisfies both the coordinate-scaled
correlation inequality and the concavity condition, which we prove for finite
temperatures. The temperature dependence differs markedly from existing thermal
GGA's.
