A point-particle treatment for the statistical mechanics of Bogomol'nyi-Pra
sad-Sommerfield (BPS) black holes in Einstein-Maxwell-dilaton theory is dev
eloped. Because of the absence of the static potential, the canonical parti
tion function for N BPS black holes can be expressed by the volume of the m
oduli space for them. We estimate the equation of state for a classical gas
of BPS black holes by the Pade approximation and find that the result agre
es with the one obtained by the mean-field approximation.