  We numerically reanalyze static and spherically symmetric black hole
solutions in an Einstein-Maxwell-dilaton system with a dilaton potential
$m_{d}^{2}\phi^{2}$. We investigate thermodynamic properties for various
dilaton coupling constants and find that thermodynamic properties change at a
critical dilaton mass $m_{d,crit}$. For $m_{d}\geq m_{d,crit}$, the black hole
becomes an extreme solution for a nonzero horizon radius $r_{h,ex}$ as the
Reissner-Nordstr\"om black hole. However, if $m_{d}$ is nearly equal to
$m_{d,crit}$, there appears a solution of smaller horizon radius than
$r_{h,ex}$. For $m_{d}<m_{d,crit}$, a solution continues to exist until the
horizon approaches zero. The Hawking temperature in the zero horizon limit
resembles that of a massless dilaton black hole for arbitrary dilaton coupling
constant.
