Extreme State of a Charged Black Hole in a Grand Canonical Ensemble

It is shown that a charged black hole in a cavity can approach the extreme state at finite temperature. In so doing, its surface area tends to that of a cavity but the proper distance L between a horizon and the boundary tends to a finite value. The arguments in the favor of zero entropy based on infinite L become inapplicable and the entropy equals the Bekenstein-Hawking one.