  A point particle treatment to the statistical mechanics of BPS black holes in
Einstein-Maxwell-dilaton theory is developed. Because of the absence of the
static potential, the canonical partition function for $N$ BPS black holes can
be expressed by the volume of the moduli space for them. We estimate the
equation of state for a classical gas of BPS black holes by Pad\'e
approximation and find that the result agrees with the one obtained by the
mean-field approximation.
