Abstract
A method is presented which allows for the computation of $〈{\ensuremath{\varphi}}^{2}〉$ for scalar fields at zero and nonzero temperatures in asymptotically flat, static, spherically symmetric spacetimes. If a spacetime has event horizons, the method works in the region exterior to the outermost event horizon. The method is used to compute $〈{\ensuremath{\varphi}}^{2}〉$ for massless and massive scalar fields in Reissner-Nordstr\om and extreme Reissner-Nordstr\om spacetimes.
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