How would you jerry-rig an android phone for continuous autonomous operation?
One thing I'd be careful not to underestimate is how hot the inside of a car can get. I've done some previous design work on GPS systems that were typically mounted under the passenger seat of a car and during summer 40 - 45 °C days the internal temperature sensor would often read around 80 °C and stay there for a significant amount of the day.

That exceeds the maximum recommended discharge / discharge temperatures of Li-Ion batteries and while many phones might be OK with it I've owned phones that won't work without a battery present presumably because they rely on it to meet short peak current demands. If parts of the battery protection circuit cut-out under high temperature it might cause problems, of course hard to know with a consumer device where you won't be privy to the exact design so you'd really need to test that side of things.

Another issue you may have is determining when the device needs a hard power reset. Software lock-ups using a watchdog are easy enough but for example my Nexus 5 seems to lose a data connection every month or two and seems to need a reboot. In normal use I can determine whether I'd expect a data connection in the location and manually restart when convenient, but doing it automatically you might end up in a situation where you're restarting often when the only real problem is the lack of signal or other connectivity issue.

In general I'd say the idea is plausible but while the upside is having very low up-front development costs the downside to using COTS consumer devices is you'll need some extensive testing to see how it performs under a variety of conditions and try a few different devices. For temperature related tests a regular oven / temperature probe does the job pretty well but for some other aspects there won't really be an alternative to long-term testing of multiple devices. 

Of course another disadvantage is that software / hardware engineering changes in new revisions of the phone in the future may cause changes in performance that you don't have control over.