Wow. I check my cooler every few times out. I would have definitely thought a high temp alarm or gauge pegged would have been seen or heard. If there is no water flow you can also hear the motor get abnormally louder, granted that the stereo is not blasting.
Sorry for your luck! A strainer has been on my list, but I have just not found a unit that is compact enough and quality built. After reading here, it seems the OEM strainer MC is putting on it's boats leaves somethings to be desired.