  We present a method for computing thermal properties of classical spin
clusters with arbitrarily chosen interactions between spins. For such systems,
instability channels are \textit{a priori} not known. The method is based on
the Fluctuating Local Field (FLF) approach, the effective description of the
system with a nonlinear and fluctuating field, and achieves substantial
improvements over mean-field theory. We show that two fluctuating modes are
sufficient for numerically accurate solution of systems consisting of two dozen
spins, while for larger systems it is needed to account for a larger number of
fluctuating modes for a full quantitative agreement with the exact solution.
