A new formulation of QCD sum rules at finite temperature (T) is developed. Because of the factorization in the operator product expansion, all the soft dynamics including the effect of finite T in the hadronic phase is taken into account in the thermal average of local operators [O]T. Unlike for the T = 0 case, [O]T has non-vanishing values for the Lorentz non-scalar operators such as qgamma(mu)D(nu)qBAR. On the basis of the observation that the finite-temperature medium can be well approximated by a dilute (non-interacting) pion gas at low T, one can make a sensible estimate of the T-dependence of various condensates, where the current algebra and the experimental information of the pion structure functions turn out to be a useful guide. We applied this method to the light vector mesons (rho, omega and A1) and found that the change of the four-quark condensate at T not-equal 0 is crucial to the change of meson properties. The lepton pair production rate from the hot hadronic medium near the rho-resonance is calculated using the result of the sum rules. This has direct relevance to the detection of the lepton pairs in future projects of the ultra-relativistic heavy-ion collisions such as RHIC and LHC.