We demonstrate the emission of highly indistinguishable photons from a quasi-resonantly pumped coupled quantum dot-microcavity system operating in the regime of cavity quantum electrodynamics. Changing the sample temperature allows us to vary the quantum dot-cavity detuning, and on spectral resonance we observe a three-fold improvement in the Hong-Ou-Mandel interference visibility, reaching values in excess of 80%. Our measurements off-resonance allow us to investigate varying Purcell enhancements, and to probe the dephasing environment at different temperatures and energy scales. By comparison with our microscopic model, we are able to identify pure-dephasing and not time-jitter as the dominating source of imperfections in our system.