  An important open question in black hole thermodynamics is about the
existence of a "mass gap" between an extremal black hole and the lightest
near-extremal state within a sector of fixed charge. In this paper, we reliably
compute the partition function of Reissner-Nordstr\"{o}m near-extremal black
holes at temperature scales comparable to the conjectured gap. We find that the
density of states at fixed charge does not exhibit a gap; rather, at the
expected gap energy scale, we see a continuum of states. We compute the
partition function in the canonical and grand canonical ensembles, keeping
track of all the fields appearing through a dimensional reduction on $S^2$ in
the near-horizon region. Our calculation shows that the relevant degrees of
freedom at low temperatures are those of $2d$ Jackiw-Teitelboim gravity coupled
to the electromagnetic $U(1)$ gauge field and to an $SO(3)$ gauge field
generated by the dimensional reduction.
