I have a 2006 HR Endeavor and have the same beeping noise coming from the dash with no warning lights coming on. I have read the threads concerning it happening in wet conditions but mine doesn't follow that reasoning.
What have have found is mine starts coming on faintly when the engine coolant temperature reaches 194 degrees. The beeping gets louder as the temperature rises. Then as the temperature starts to cool down again, as in coming down a grade, the beeping becomes fainter and fainter until the temperature is below 194 degrees.
This is very annoying since my motorhome does have the Aladdin system and I can monitor my engine temperature through that versus just a dash gauge. The Cummins manual states that 220 degrees is the max you should go and I have never come close to that.
Paul