  A method is given to compute an approximation to the noise kernel, defined as
the symmetrized connected 2-point function of the stress tensor, for the
conformally invariant scalar field in any spacetime conformal to an
ultra-static spacetime for the case in which the field is in a thermal state at
an arbitrary temperature. The most useful applications of the method are flat
space where the approximation is exact and Schwarzschild spacetime where the
approximation is better than it is in most other spacetimes. The two points are
assumed to be separated in a timelike or spacelike direction. The method
involves the use of a Gaussian approximation which is of the same type as that
used by Page to compute an approximate form of the stress tensor for this field
in Schwarzschild spacetime. All components of the noise kernel have been
computed exactly for hot flat space and one component is explicitly displayed.
Several components have also been computed for Schwarzschild spacetime and
again one component is explicitly displayed.
