I don't know if these are related but... We took a trip from L.A. to Sedona AZ two weeks ago during the top of the heat wave. 120 degrees in Needles and 108 in Sedona for three days we were there. The car sat in the sun at the motel all three days except for one short hiking trip. Everything was fine, car ran great, and I didn't baby it, pretty much 75mph all the way there average. On the day we were leaving I went out to get prepared to leave and there was a distinct HUM coming from the rear, most probably the battery area. After a drive to the gas station and on our way out it resided, but I was concerned. Never heard this sound before. Second thing is (twice I've noticed this), very hot days, I'm getting a lull in acceleration from stop. Whether in Normal or Power mode it's the same. (I regularly drive in Power mode). When hitting the pedal it *pauses* before it accelerates away, like when you start running out of gas in a gas vehicle. 2010 Prius 2 with 68000 miles. Still under certified warranty plus extended warranty. If there's something going haywire I want to address this soon. I'm all ears here...
In power mode there is a very large and very short (up to 100 amps for one second or so) burst of power from the battery that fills in that gap. My guess, just off the top of my head, is that the car does not allow this when the battery is at a very high temp in order to protect it. Especially if the problem goes away once you have been driving a while and the car starts cooling off inside. You might also notice it running the engine when it might otherwise not do so if this is the reason. I also run almost exclusively in power mode and have a scangauge that I have observed these things with.
Most gas tank systems have a non-electric vent mechanism that'll activate if it's really hot and air pressure is building up in the tank. Might be the hum you heard, not sure.
Yes, I did test it in Normal mode, still a bit of a lull, but maybe not as severe. Considering the heat we've had, still, this is a 'new' issue that's just started.
I have not had that happen, but my battery temp hasn't gotten above 109 F or so (I live in Texas but it's in the garage at home and at work), which I think is below the threshold for battery protection mode. If your battery is at 125 F, for example, it's possible that these things are normal behavior. But without a scanning device you can't be sure. With the extended warranty you have I would just take it in and let them check in.
By any chance, was this about 5 hours after the car was previously used? There is an automatic evaporative fuel system thingy operation at about this time, not related to the outside weather. By any chance, was this during engine warmup, in the first half mile from a cold start? If so, it sounds normal. Never mind hot outdoor temperatures, those are still cold to the engine.
Q1 - The car sat overnight after being used the previous afternoon. Q2 - I would say yes, I hop in and leave the parking lot because it's a hot place, no shade. It was noticeable immediately from the git go. The pause in acceleration tapered off slightly on the drive home which is about 10 miles.
The portion that happens immediately from the git go, and then tapers away after a minute or two of ICE warmup, would be the portion I describe as normal. Whatever remains after that is not normal.
That's definitely true about the engine, but not the battery, which the car seems to want to run at 75-95F. 110+ degrees may cause different behavior as the car protects it.