  We describe the use of the exact Yang-Yang solutions for the one-dimensional
Bose gas to enable accurate kinetic-energy thermometry based on the
root-mean-square width of an experimentally measured momentum distribution.
Furthermore, we use the stochastic projected Gross-Pitaevskii theory to provide
the first quantitative description of the full momentum distribution
measurements of Van Amerongen et al., Phys. Rev. Lett. 100, 090402 (2008). We
find the fitted temperatures from the stochastic projected Gross-Pitaevskii
approach are in excellent agreement with those determined by Yang-Yang
kinetic-energy thermometry.
