Yes, thermal cut back is pretty much what all of your described. My car will sometimes get to the point where it will even stop auto stopping so that that initial draw to turn the engine on won't add unnecessary heat to the batteries. When it cuts back the thing that makes me mad at it is that it will keep assisting at normal rates. At that point it only makes the problem worse and it will even give full assist if you floor it. I guess this might be for reliability purposes as what if you got in a situation where you needed that full power to get out of a jam and it wasn't there.
The thing is I really don't get recalibrations (I did induce one once after the cut back happened the first time thinking it was way overcharged or something... only made it worse), it just goes in to cut back if it wants to. This is probably the cars second summer, my first full one with it, I got it back in last august. I'm gonna venture, sno, to say that your battery recalibrations can be attributed to heat, even if your parked inside all the time, which should help a lot, but when you drive the batteries and everything in that box get hot. Seriously, try using the air for a week, it will probably help your recalibration situation. Then again the damage might already be done.
The thing is I've seen two other cars that have been in Phoenix do this as well. The previous owner of one finally got sick and tired of it and got rid of the car. He told me that everything I'm experiencing happened to his car. Honestly I'm scared because as much as I like the car if it keeps doing all this it's not staying around. Again, relating back to the sticker on the inside of the door panel. Do not bake the car over 149 degrees when painting... well the inside of a car will easily get to 175 in the summer here. I guess I just can't win can I?