When electric motors in good mechanical condition "overheat", does this imply that that they must be drawing more than their rated amps?

The question occurs to me while I'm working on my evaporative cooler, but it seems applicable to motors found in power tools. It would be comforting to know that any tool motor that was drawing its proper amps should be working against the proper load and running at its proper temperature. (I just got a new AC ammeter.) Sounds too simple to be true.