  We compute the renormalized expectation value of the square of a quantum
scalar field on a Reissner-Nordstrom-de Sitter black hole in which the
temperatures of the event and cosmological horizons are equal (`lukewarm' black
hole). Our numerical calculations for a thermal state at the same temperature
as the two horizons indicate that this renormalized expectation value is
regular on both the event and cosmological horizons. We are able to show
analytically, using an approximation for the field modes near the horizons,
that this is indeed the case.
