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The Hadamard renormalization prescription is used to derive a two dimensionalanalog of the renormalized stress tensor for a minimally coupled scalar fieldin Schwarzschild-de Sitter space time. In the two dimensional analog theminimal coupling reduces to the conformal coupling and the stress tensor isfound to be determined by the (nonlocal) contribution of the anomalous traceand some additional parameters in close relation to the work [1]. To properlyrelate the stress tensor to the state of outwards signals coming from thedirection of the black hole at late times we propose a cut-off hypothesis whichexcludes the contribution of the anomalous trace close to the black holehorizon. The corresponding cut-off scale is found to be related to theequilibrium-temperature of the cosmological horizon in a leading orderestimate. Finally, we establish a relation between the radiation-temperature ofthe black hole horizon at large distance from the hole and the the anomaloustrace and determine the correction term to the Hawking temperature due to thepresence of the cosmological horizon.Comment: To appear in Phys. Rev. D 56, 1 (1997

Hadamard renormalization, conformal anomaly, and cosmological event horizons