Why does my Nexus 5 slow down, freeze, and then reboot?

A few weeks ago my Nexus 5 started frequently slowing down (over the course of 5-20sec) then freezing and promptly rebooting (or turning off completely).

I first assumed it to be the power switch because I've had another Nexus 5 with that issue and similar symptoms. Though replacing the power switch didn't help, so it's not that.

I've also tried restoring from factory settings (via the recovery console) but the behavior returned.

The symptoms point to hardware... but I'm really at a loss as to what the problem would be. Any ideas? Or perhaps additional places to look for more info?