  We consider a quantum field which is in a Hartle-Hawking state propagating in
a spherically symmetric black hole space-time. We calculate the components of
the stress tensor, renormalized using the Hadamard form of the Green's
function, in the exterior region of this space-time. We then specialize these
results to the case of the `lukewarm' Riessner-Nordstrom-de Sitter black hole.
