I used to have motor, controller, and battery temps showing on the app but I eventually whittled it down to the motor as the others never reached any significant temp. (I'm on an FX, could vary by bike.) I didn't have the phone on when I was hillclimbing but I'd be surprised if it was suddenly another component.
As for cool temps, the difference between 30F and 70F isn't much compared to the ~230F limit, it might buy you some time but not a lot. Mostly mornings these days I'm riding in at ~50F. I am concerned I'll hit the limit even faster once it's 80F+ this summer!
It cools down pretty quickly when you keep the power off for a moment, so I think even a smallish amount of airflow could make a significant difference. Also I already have about a dozen computer fans from 60mm to 120mm lying around so I might as well give them a shot! Unfortunately the mega-hills are far from home so I can really only test the highway overheating. I have some pretty extreme roads (CA-130 up Mt. Hamilton to Lick Observatory) in my backyard but temp has never been a problem there, probably because speeds are higher and power isn't quite as constant. I have been to Hollister OHV area yet, maybe there are some continuous climbs there but probably not Mendocino Ntnl Forest level.
Indeed liquid cooling makes all the difference for these edge cases, and keeps things more evenly cooled which is good for longevity. Not so easy to add to an existing finned case though, and I am riding the line close enough with my warranty I don't need to be disassembling the motor!