  We present the results of an extension of our previous work on large-scale
simulations of dynamically triangulated toroidal random surfaces embedded in
$R^3$ with extrinsic curvature. We find that the extrinsic-curvature specific
heat peak ceases to grow on lattices with more than 576 nodes and that the
location of the peak $\lam_c$ also stabilizes. The evidence for a true
crumpling transition is still weak. If we assume it exists we can say that the
finite-size scaling exponent $\frac {\alpha} {\nu d}$ is very close to zero or
negative. On the other hand our new data does rule out the observed peak as
being a finite-size artifact of the persistence length becoming comparable to
the extent of the lattice.
