Quantum emitters in hexagonal boron nitride (hBN) are emerging as bright and robust sources of single photons for applications in quantum optics. In this work we present detailed studies on the limiting factors to achieve Fourier transform limited spectral lines. Specifically, we study phonon dephasing and spectral diffusion of quantum emitters in hBN via resonant excitation spectroscopy at cryogenic temperatures. We show that the linewidths of hBN quantum emitters are phonon broadened, even at 5 K, with typical values of the order of ∼1GHz. While spectral diffusion dominates at increasing pump powers, it can be minimized by working well below saturation excitation power. Our results are important for future utilization of quantum emitters in hBN for quantum interference experiments.