  We study a multi-matrix model whose low temperature phase is a fuzzy sphere
that undergoes an evaporation transition as the temperature is increased. We
investigate finite size scaling of the system as the limiting temperature of
stability of the fuzzy sphere phase is approached. We find on theoretical
grounds that the system should obey scaling with specific heat exponent
\alpha=1/2, shift exponent \bar \lambda=4/3 and that the peak in the specific
heat grows with exponent \bar \omega=2/3. Using hybrid Monte Carlo simulations
we find good collapse of specific heat data consistent with a scaling ansatz
which give our best estimates for the scaling exponents as \alpha=0.50 \pm
0.01,\bar \lambda=1.41 \pm 0.08 and \bar \omega=0.66 \pm 0.08 .
