Nexus 5 rebooting randomly

Thanks for your answers. I am just curious though: if the power button is the culprit, why would the reboots become more frequent the longer the phone is kept on? When I first turn it on after it's been off for a long time, it will work for about 10 minutes, then reboot itself, then work for for another 5 minutes, reboot, work for 2 minutes, and then start rebooting constantly. This pattern occurs every time it's turned on from "cold" state. To me this sounds like an overheating issue somewhere, but the phone does not actually overheat. I even tried replacing the battery, as I had a similar problem with another phone which I was able to trace to a bad battery. But here the battery was not the issue. So why would a shorted power button cause a pattern like that?

P.S. I am not particularly handy with a soldering iron, so I am trying to exhaust my other options before replacing the power button. And also - to use the opportunity to improve my understanding of how phone components actually work.