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Let $k$ be a $p$-adic field. Let $G$ be the group of $k$-rational points of a connected reductive group $𝖦$ defined over $k$, and let $𝔤$ be its Lie algebra. Under certain hypotheses on $𝖦$ and $k$, wethe tempered dual $\widehat{G}$ of $G$ via the Plancherel formula on $𝔤$, using some character expansions. This involves matching spectral decomposition factors of the Plancherel formulas on $𝔤$ and $G$. As a consequence, we prove that any tempered representation contains a good minimal $𝖪$-type; we extend this result to irreducible admissible...