We have studied spectral diffusion of the photoluminescence of a single CdSe quantum dot inserted in a ZnSe nanowire. We have measured the characteristic diffusion time as a function of pumping power and temperature using a recently developed technique [G. Sallen et al, Nature Photon. \textbf{4}, 696 (2010)] that offers subnanosecond resolution. These data are consistent with a model where only a \emph{single} carrier wanders around in traps located in the vicinity of the quantum dot.
