The P3 battery is almost certainly a different chemistry than the P2 battery.
Charge volts per cell: P3= 4.375v; P2= 4.20v
Reported volts/cell charged: P3= 4.35; P2= 4.18v
My first flight in my P3 resulted in an "almost too hot to touch" battery. But after 5 flights, it's coming out much cooler. I don't know if that's breaking it in, but I suspect it is getting the internal chemical structures "lined up" for better conductance by cycling it.
By the way- I'm not following the "only discharge 1/2 way for 10 cycles" regimen. These batteries are only discharging at a bit over 3C. That's not taxing them at all. I think DJI has done a lot of homework in the development of these "smart" batteries. They say to discharge the batteries all the way after 10 cycle until the P3 won't turn on. That just seems inconsistent with the "baby the new battery" approach.
Now to Adam's problem. I think he's right. It appears the recharge temperature limit is too aggressive. Might be variation in the sensitivity of the sensor from one battery to another. Maybe it can be changed with a battery firmware update. We won't know until more batteries get into people's hands.
I think so many people are doing the 10 minute thing that their batteries aren't getting hot enough to get to the issue... so I bet we won't get the angry beavers attacking this board until June. Especially when the other batteries are in and people are trying to hot swap. It just can't be an hour wait. That takes the number of batteries I need from 4 to 8. That's kinda goofy.