  Thermal fluctuations of a massive scalar field in the Rindler wedge have been
recently obtained. As a by product, the Minkowski vacuum fluctuations seen by a
uniformly accelerated observer have been determined and confronted with the
corresponding Minkowski thermal fluctuations of the same field, seen by an
inertial observer. Since some of the calculations of this previous work have
not been detailed on it, and they present some important subtleties, they are
explicitly done here. These subtleties have to do with the leading order
behaviour of certain parameter dependent integrals. Some of the leading order
expansions are derived using the Riemann-Lebesgue lemma.
