The present study reports on the temperature dependent pyroelectric coefficient of free-standing and strain-free gallium nitride (GaN) grown by hydride vapor phase epitaxy (HVPE). The Sharp-Garn method is applied to extract the pyroelectric coefficient from the electrical current response of the crystals subjected to a sinusoidal temperature excitation in a range of 0 °C to 160 °C. To avoid compensation of the pyroelectric response by an internal conductivity, insulating GaN crystals were used by applying C, Mn, and Fe doping during HVPE growth. The different pyroelectric coefficients observed at room temperature due to the doping correlate well with the change of the lattice parameter c. The obtained data are compared to previously published theoretical and experimental values of thin film GaN and discussed in terms of a strained lattice.