Within a chiral model which provides a good description of the properties of rho and a1 mesons in vacuum, it is shown that, to order T2, the rho- and a1-meson masses remain constant in the chiral limit, even if at tree level they are proportional to the chiral condensate, sigma0. 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