We propose a temporally multiplexed version of the Duan-Lukin-Cirac-Zoller (DLCZ) quantum-repeater protocol using controlled inhomogeneous spin broadening in atomic gases. A first analysis suggests that the advantage of multiplexing is negated by noise due to spin-wave excitations corresponding to unobserved directions of Stokes photon emission. However, this problem can be overcome with the help of a moderate-finesse cavity which is in resonance with Stokes photons, but invisible to the anti-Stokes photons. Our proposal promises greatly enhanced quantum repeater performance with atomic gases.