  Thermal fluctuations for a massive scalar field in the Rindler wedge are
obtained by applying the point-splitting procedure to the zero temperature
Feynman propagator in a conical spacetime. Renormalization is implemented by
removing the zero temperature contribution. It is shown that for a field of non
vanishing mass the thermal fluctuations, when expressed in terms of the local
temperature, do not have Minkowski form. As a by product, Minkowski vacuum
fluctuations seen by an uniformly accelerated observer are determined and
confronted with the literature.
