Recent work has suggested that an additional ≲6.9 eV per baryon of heating in the intergalactic medium is needed to reconcile hydrodynamical simulations with Lyman-α forest absorption line widths at redshift z≃0.1. Resonant conversion of dark photon dark matter into low frequency photons is a viable source of such heating. We perform the first hydrodynamical simulations including dark photon heating and show that dark photons with mass m_{A^{'}}∼8×10^{-14} eV c^{-2} and kinetic mixing ε∼5×10^{-15} can alleviate the heating excess. A prediction of this model is a nonstandard thermal history for underdense gas at z≳3.