  The vector and axial vector current mixing phenomena at low temperature pion
gas by Dey, Eletsky and Ioffe, leads to the low temperature correction of the
photon-vector meson coupling ($g_\rho$) at order $\epsilon=T^2/6f_\pi^2$ and
the $\rho$ meson mass at order $\epsilon^2$. We show how this {\it low
temperature theorems} involving the photon and vector mesons are satisfied in
the chiral models based on hidden gauge symmetry and the massive Yang-Mills
approach with an explicit $a_1$ meson. We discuss possible phenomenological
consequences of the low temperature corrections in RHIC experiments.
