Navigating the site I see reboot questions are common, and there are two main suggestions for log viewing: (1) adb, which requries a computer nearby, and (2) aLogrec, which seems to not be working for 4.x according to reviews in the Play Store.
As it happens, I'm having this problem, but only when I'm out on the street, only around noon, only in certain parts of the city, and usually when I have BeyondPod playing in the background and/or Ingress running on the foreground. Usually the first reboot happens when both are running, then I try to use whichever I want the most at the moment, and it almost always fails, rebooting within seconds after I open either app.
My first thought was temperature (I live at latitude 11°S), but these reboots happen even when I stand in the shadow at windy spots. To compare, I've seen my phone withstand at least 10 Kelvin (18F) worse when I play other 3D games at home, that do heat it from sheer processing.
Storage is about half full, so is RAM. Processing, again, I've done much worse to my phone at home. I'm simply out of ideas to guess. I need some way to collect log data.