In my humble opinion I think that it's probably an electrical problem.  The
chances of the engine coolant temp changing that drastically in such a short
period of time is pretty much nil.  It really could be anything.  The
climate control system might have a bad ground and it is "stealing" the
ground from the cluster.  Again I'm not sure this is what's happening, but
it is a possibility.  I've seen a bad headlight ground cause the turn signal
indicator to come on and still light up the headlight.  That was no fun to
figure out.
I guess my advice would to be to take it to someone who has a good
understanding of auto electrical systems and the proper tools and diagrams
for your car.