Bill,
Yes the engine thermostat does open and close to maintain the engine temperature, and yes a thermostat failure on a fairly new Cat engine is rare, but it does happen. However, the reason that I said that there was almost no chance that a defective thermostat was causing the overheat problem in this case, is because of the conditions under which it happened.
The coach overheats only on a grade if the coach is not downshifted to bring up the RPMs, and the condition can be duplicated under the same conditions, but the coach does not overheat at any other times. If a thermostat was sticking, it would not only stick under a very specific set of conditions, and stick every time that those conditions exist. The thermostat is a heat regulated mechanical valve that has no way of detecting whether you are climbing a hill or not.
Gerald