  Within a chiral model which provides a good description of the properties of
rho and a_1 mesons in vacuum, it is shown that, to order T^2, the rho- and
a_1-meson masses remain constant in the chiral limit, even if at tree level
they are proportional to the chiral condensate, sigma_0. Numerically, the
temperature dependence of the masses turns out to be small also for realistic
parameter sets and high temperatures. The weak temperature dependence of the
masses is consistent with the Eletsky-Ioffe mixing theorem, and traces of
mixing effects can be seen in the spectral function of the vector correlator at
finite temperature.
