Engine Turns on When Battery is FULL

Hi folks! I have been a member of this forum since it began (or close to it). I always check in periodically since I STILL have my 2004 Prius which currently has 264,xxx miles. The car runs very well (at least I think it does). I have always maintained it beyond what was required. Anyway, it has been very, very hot lately in south Florida (high 90's plus 50% humidity) so I do not know if that has anything to do with my problem. I have noticed that after I have driven the car for a while the engine periodically turns itself on when I am at a stoplight even though the battery shows practically full (full blue). The engine will continue to stay on until I resume driving. I have the AC on full blast as it is needed to keep the cabin cool. Otherwise, the car seems to be performing satisfactorily.

 

Thanks for all your replies. I am thinking that the previous poster hit it on the nail. I haven't driven the car today but I'll monitor it next week. On a happy note, I continue to be amazed at how well my car performs as it turns 264,000 miles. Never in my life did I expect this car to last me this long. I don't want to jinx myself but I've hardly put any money into the car except maintenance and some long term replacements (shocks/springs), tie rods, and a few other odds and ends.