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Let G be an orthogonal or symplectic p-adic group (not necessarily split) oran inner form of a general linear p-adic group. In a previous paper, it wasshown that the Bernstein components of the category of smooth representationsof G are equivalent to the category of right modules over some Hecke algebrawith parameters, or more general over the semi-direct product of such analgebra with a finite group algebra. The aim of the present paper is to showthat this equivalence preserves the tem- pered spectrum and the discrete seriesrepresentations.

Alg\`ebres de Hecke avec param\`etres et repr\'esentations d'un groupe p-adique classique: pr\'eservation du spectre temp\'er\'e