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iPhones stored for forensic analysis unexpectedly reboot, causing problems for officials
(appleinsider.com)
This is a most excellent place for technology news and articles.
I wouldn't mind having the ability to schedule a reboot on my phone as an extra precaution.
It probably requires root, but I'm sure Tasker can do this.
Really, all phones should have the option to reboot into locked mode on certain conditions like being taken out of network or being unattended for a while.
Could possibly also look at the motion sensors to see if it is in a pocket moving around or if it was sitting around for a while.
Good idea, but a motivated attacker could put them on one of those rocker tables like they use for mixing blood. It also wouldn't cover the more common scenario of someone stealing it out of your hand.