Massless particles, including photons, are not governed by particle conservation law during their typical interaction with matter even at low energies and thus have no chemical potential. However, in driven systems, near-equilibrium dynamics can lead to equilibration of photons with a finite number, describable using an effective chemical potential [M. Hafezi et al., Phys. Rev. B 92, 174305 (2015)]. Here we build upon this general concept with an implementation appropriate for a photon-based quantum simulator. We consider how laser cooling of a well-isolated mechanical mode can provide an effective low-frequency bath for the quantum simulator system. We show that the use of auxiliary photon modes, coupled by the mechanical system, enables control of both the chemical potential and temperature of the resulting photonic quantum simulator s grand canonical ensemble.