Pyroelectric materials convert fluctuating heat flows to electrical energy. The most efficient pyroelectric materials are inorganic ferroelectrics, that is, materials showing spontaneous, switchable electric polarization. We have developed a computational methodology to study the atomic-level mechanisms of pyroelectricity in inorganic ferroelectrics. We determine the primary pyroelectric coefficients by combining hybrid density functional calculations with self-consistent phonon theory and the Berry phase approach for polarization. Secondary pyroelectric coefficients are evaluated by combining thermal properties from quasi-harmonic approximation with elastic and piezoelectric coefficients.