  The fluctuating and dissipative dynamics of matter-wave dark solitons within
harmonically trapped, partially condensed Bose gases is studied both
numerically and analytically. A study of the stochastic Gross-Pitaevskii
equation, which correctly accounts for density and phase fluctuations at finite
temperatures, reveals dark soliton decay times to be lognormally distributed at
each temperature, thereby characterizing the previously predicted long lived
soliton trajectories within each ensemble of numerical realizations (S.P.
Cockburn {\it et al.}, Phys. Rev. Lett. 104, 174101 (2010)). Expectation values
for the average soliton lifetimes extracted from these distributions are found
to agree well with both numerical and analytic predictions based upon the
dissipative Gross-Pitaevskii model (with the same {\it ab initio} damping).
Probing the regime for which $0.8 k_{B}T < \mu < 1.6 k_{B}T$, we find average
soliton lifetimes to scale with temperature as $\tau\sim T^{-4}$, in agreement
with predictions previously made for the low-temperature regime $k_{B}T\ll\mu$.
The model is also shown to capture the experimentally-relevant decrease in the
visibility of an oscillating soliton due to the presence of background
fluctuations.
