Atoms trapped in the evanescent field around a nanofiber experience strong coupling to the light guided in the fiber mode. However, due to the intrinsically strong positional dependence of the coupling, thermal motion of the ensemble limits the use of nanofiber trapped atoms for some quantum tasks. We investigate the thermal dynamics of such an ensemble by using short light pulses to make a spatially inhomogeneous population transfer between atomic states. As we monitor the wave packet of atoms created by this scheme, we find a damped oscillatory behavior which we attribute to sloshing and dispersion of the atoms. Oscillation frequencies range around 100 kHz, and motional dephasing between atoms happens on a timescale of 10 $mu$s. Comparison to Monte Carlo simulations of an ensemble of 1000 classical particles yields reasonable agreement for simulated ensemble temperatures between 25 $mu$K and 40 $mu$K.
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