  We study the derivation of the Gibbs measure for the nonlinear
Schr\"{o}dinger equation (NLS) from many-body quantum thermal states in the
high-temperature limit. In this paper, we consider the nonlocal NLS with
defocusing and unbounded $L^p$ interaction potentials on $\mathbb{T}^d$ for
$d=1,2,3$. This extends the author's earlier joint work with Fr\"{o}hlich,
Knowles, and Schlein, where the regime of defocusing and bounded interaction
potentials was considered. When $d=1$, we give an alternative proof of a result
previously obtained by Lewin, Nam, and Rougerie.
  Our proof is based on a perturbative expansion in the interaction. When
$d=1$, the thermal state is the grand canonical ensemble. As in the author's
earlier joint work with Fr\"{o}hlich, Knowles, and Schlein, when $d=2,3$, the
thermal state is a modified grand canonical ensemble, which allows us to
estimate the remainder term in the expansion. The terms in the expansion are
analysed using a graphical representation and are resummed by using Borel
summation. By this method, we are able to prove the result for the optimal
range of $p$ and obtain the full range of defocusing interaction potentials
which were studied in the classical setting when $d=2,3$ in the work of
Bourgain.
