  We construct explicit mode expansions of various tree-level propagators in
the Rindler -- de Sitter universe, also known as the static (or compact) patch
of the de Sitter spacetime. We construct in particular the Wightman functions
for thermal states having a generic temperature $T$. We give a fresh simple
proof that the only thermal Wightman propagator that respects the de Sitter
isometry is the restriction to the Rindler -- de Sitter wedge of the propagator
for the Bunch--Davies state. It is the thermal state with $T = (2 \pi)^{-1}$ in
the units of de Sitter curvature. We show that propagators with
$T\ne(2\pi)^{-1}$ are only time translation invariant and have extra
singularities on the boundary of the static patch. We also construct the
expansions for the so-called alpha-vacua in the static patch and discuss the
flat limit.
