  I discuss the trace of a heat kernel Tr[e^(-tA)] for compact fuzzy spaces. In
continuum theory its asymptotic expansion for t -> +0 provides geometric
quantities, and therefore may be used to extract effective geometric quantities
for fuzzy spaces. For compact fuzzy spaces, however, an asymptotic expansion
for t -> +0 is not appropriate because of their finiteness. It is shown that
effective geometric quantities are found as coefficients of an approximate
power-law expansion of the trace of a heat kernel valid for intermediate values
of t. An efficient method to obtain these coefficients is presented and applied
to some known fuzzy spaces to check its validity.
