  We develop finite temperature theory for a trapped dipolar Bose gas including
thermal exchange interactions. Previous treatments neglected these, difficult
to compute, terms. We present a methodology for numerically evaluating the
thermal exchange contributions, making use of cylindrical symmetry. We then
investigate properties of the dipolar gas, including calculating the excitation
spectrum over the full range of trap anisotropy. We evaluate the contributions
due to thermal exchange noting that, under some regimes, these effects can be
at least as significant as the direct interaction. We therefore provide
guidance as to when these cumbersome terms can be neglected and when care
should be exercised regarding their omission.
