We use a phase field crystal model to generate large-scale bicrystalline and polycrystalline single-layer hexagonal boron nitride (h-BN) samples and employ molecular dynamics (MD) simulations with the Tersoff many-body potential to study their heat transport properties. The Kapitza thermal resistance across individual h-BN grain boundaries is calculated using the inhomogeneous nonequilibrium MD method. The resistance displays strong dependence on the tilt angle, the line tension and the defect density of the grain boundaries. We also calculate the thermal conductivity of pristine h-BN and polycrystalline h-BN with different grain sizes using an efficient homogeneous nonequilibrium MD method. The in-plane and the out-of-plane (flexural) phonons exhibit different grain size scalings of the thermal conductivity in polycrystalline h-BN and the extracted Kapitza conductance is close to that of large-tilt-angle grain boundaries in bicrystals.