A standard plane-wave expansion method is used to investigate temperature and applied hydrostatic pressure dependence of the photonic band structure of a two-dimensional honeycomb lattice composed by cylindrical rods of GaAs, embedded in air. Present results suggest that for H-polarization an increment of hydrostatic pressure and temperature not only shifts the photonic band gaps, but diminish the energy width of the second and upper band gaps, while for E-polarization the first band gap is shifted to higher energies, without modifying the width of the other band-gaps, consequently modifying the tunability of this system.