  The semi-classical Hawking evaporation process of Reissner-Nordstr\"om black
holes is analyzed. It is shown that this quantum mechanism may turn a
near-extremal black-hole spacetime with $T_{\text{BH}}\lesssim \hbar^2/G^2M^3$
into an horizonless naked singularity, thus violating the Penrose cosmic
censorship conjecture. It is therefore conjectured that, within the framework
of a self-consistent quantum theory of gravity, the Bekenstein-Hawking
temperature should be bounded from below by the simple relation
$T_{\text{BH}}\gtrsim \hbar^2/G^2M^3$.
