  The decay of a vortex from a non-rotating high temperature Bose-Einstein
condensate (BEC) is modeled using the stochastic projected Gross-Pitaevskii
equation (SPGPE). In order to exploit the tunability of temperature in SPGPE
theory while maintaining the total atom number constant, we develop a simple
and accurate Hartree-Fock method to estimate the SPGPE parameters for systems
close to thermal equilibrium. We then calculate the lifetime of a vortex using
three classical field theories that describe vortex decay in different levels
of approximation. The SPGPE theory is shown to give the most complete
description of the decay process, predicting significantly shorter vortex
lifetimes than the alternative theories. Using the SPGPE theory to simulate
vortex decay for a trapped gas of $5\times 10^5$ $^{87}$Rb atoms, we calculate
a vortex lifetime $\bar{t}$ that decreases linearly with temperature, falling
in the range 20{\rm s}$ >\bar{t} >$1.5{\rm s} corresponding to the temperature
range $0.78T_c\leq T\leq0.93T_c$. The vortex lifetimes calculated provide a
lower bound for the lifetime of a persistent current with unit winding number
in our chosen trap geometry, in the limit of vanishing vortex pinning
potential.
