It was recently demonstrated that one can reconstruct the impulse response between passive sensors by cross-correlating diffuse waves or ambient noise. Using seismic waves recorded on the moon, we show here that not only direct waves can be retrieved, but also late arrivals that have been scattered before reaching the seismometers. As these late arrivals propagate for a longer time, they are more sensitive to weak perturbations of the medium such as velocity changes. This high sensitivity of scattered waves is used to monitor periodic velocity changes in the lunar soil by measuring small delays of the passively retrieved coda waves. The velocity changes result from temperature variations due to periodic heating of the lunar surface by the sun.