  We study link-diluted $\pm J$ Ising spin glass models on the hierarchical
lattice and on a three-dimensional lattice close to the percolation threshold.
We show that previously computed zero temperature fixed points are unstable
with respect to temperature perturbations and do not belong to any critical
line in the dilution-temperature plane. We discuss implications of the presence
of such spurious unstable fixed points on the use of optimization algorithms,
and we show how entropic effects should be taken into account to obtain the
right physical behavior and critical points.
