  It has been observed that for black holes in certain family of Horndeski
gravity theories Wald's entropy formula does not lead to the correct first law
for black hole thermodynamics. For this family of Horndeski 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. We show
that the temperature of the black hole should be modified from surface gravity
over $2\pi$ to include effects of this effective metric. The modified
temperature, with the entropy unambiguously computed by the solution phase
space method, yields the correct first law. Our results have far reaching
implications for the Hawking radiation and species problem, going beyond the
Horndeski theories.
