message dash says, "AC/Off Due To High Engine Temperture"

What is your question?

With this message on, the temp gauge shows "cold", ac blows warm air and cooling fan runs continuely with engine off. I had this same problem two months ago. Dealer replaced themostat everything went back to normal. Recently, the message reappeared and same problems reoccur. While driving with message on, it then disappears and car back to normal - temp gauge working properly, ac starts blowing cold air and cooling fan stops with engine off. Car shows no sign of overheating.

What makes this problem better or worse?

nothing

How long has your 2010 Chevrolet Equinox had this problem?

two months