Hmm, well I was thinking a misbehaving app which, it just may be but you state no recent apps. However, I wouldn't rule that out.
Now, back to your original inquiry, I'm sure there is a no-root logging app you could try but honestly I don't know much about what is out there. Long ago when I was rooted, I used aLogCat app or CatLog app. Decent apps for sure but again, required root.
Perhaps someone else can shed some light on what other ideas, or apps there are for logging, or the reason for your reboots.
Trying to put myself in your shoes, I would perhaps disable the last app you installed to see if that at least helps.
Question, about how many times a day does this happen? Or is that hit and miss too?