  We probe the indistinguishability of photons emitted by a semiconductor
quantum dot (QD) via time- and temperature- dependent two-photon interference
(TPI) experiments. An increase in temporal-separation between consecutive
photon emission events, reveals a decrease in TPI visibility on a nanosecond
timescale, theoretically described by a non-Markovian noise process in
agreement with fluctuating charge-traps in the QD's vicinity. Phonon-induced
pure dephasing results in a decrease in TPI visibility from $(96\pm4)\,$\% at
10\,K to a vanishing visibility at 40\,K. In contrast to Michelson-type
measurements, our experiments provide direct access to the time-dependent
coherence of a quantum emitter at a nanosecond timescale.
