Using scanning tunneling spectroscopy, we investigated the temperature dependence of the quasiparticle density of states of overdoped Bi2Sr2CuO6+δ between 275 mK and 82 K. Below Tc=10K, the spectra show a gap with well-defined coherence peaks at ±Δp≃12meV, which disappear at Tc. Above Tc, the spectra display a clear pseudogap of the same magnitude, gradually filling up and vanishing at T∗≃68K. The comparison with Bi2Sr2CaCu2O8+δ demonstrates that the pseudogap and the superconducting gap scale with each other, providing strong evidence that they have a common origin.