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We derive the finite temperature conductance peak distributions andpeak-to-peak correlations for quantum dots in the Coulomb blockade regimeassuming the validity of random matrix theory. The distributions are universal,depending only on the symmetry class and the temperature measured in units ofthe mean level spacing, $\Delta$. When the temperature is comparable to$\Delta$ several resonances contribute to the same conductance peak and we findsignificant deviations from the previously known $T \ll \Delta$ distributions.In contrast to the $T \ll \Delta$ case, these distributions show a strongsignature of the charging energy and charge quantization on the dot.Comment: 14 pages, 3 Postscript figures included, RevTex, to appear as a Rapid  Communication in Physical Review

Conductance peak distributions in quantum dots at finite temperature: Signatures of the charging energy