Horndeski theories are the most general family of scalar-tensor gravity with second order equations of motion. In these theories speeds of propagation of gravitons and photons are in general different and gravitons move on an effective metric different than the one seen by photons. These theories admit black hole solutions with the peculiar feature that they do not satisfy the first law with the entropy given by the Wald formula. We argue that the issue with the first law stems from the fact that black hole temperature is not given by the surface gravity of the black hole metric, but with the surface gravity of the effective metric seen by gravitons. The modified temperature, with the entropy unambiguously computed by the solution phase space method, yields the correct first law. We discuss far-reaching implications of our results for black hole thermodynamics beyond the Horndeski theories.
