  The Fortuin-Kasteleyn and heat-bath damage spreading temperatures T_{FK}(p)
and T_{ds}(p) are studied on random bond Ising models of dimension two to five
and as functions of the ferromagnetic interaction probability p; the conjecture
that T_{ds}(p) ~ T_{FK}(p) is tested. It follows from a statement by Nishimori
that in any such system exact coordinates can be given for the intersection
point between the Fortuin-Kasteleyn T_{FK}(p) transition line and the Nishimori
line, [p_{NL,FK},T_{NL,FK}]. There are no finite size corrections for this
intersection point. In dimension three, at the intersection concentration
[p_{NL,FK}] the damage spreading T_{ds}(p) is found to be equal to T_{FK}(p) to
within 0.1%. For the other dimensions however T_{ds}(p) is observed to be
systematically a few percent lower than T_{FK}(p).
