A new Nature highlight of a GRL article discusses attempts made to reconstruct temperature records from the battery temperatures of smartphones. Since smartphones natively keep track of their battery temperature for safety purposes, they also help to keep track of the external temperature. This is used to obtain temperature in the "urban canopy", aka the low atmospheric boundary layer in which humans live that is often much warmer than the atmosphere just a few tens of meters high.
Whether this will actually work is a secondary question, because at best battery temperatures are a poor proxy for atmospheric temperature. They are altered by not only the ambient temperature but the physical location (inside, outside, in a pocket, in direct sunlight) of the phone, as well as the memory/CPU usage of the phone. Overeem (not this guy) et al. used a "straightforward heat transfer model" to gauge air temperature.
With T0 a constant equilibrium temperature, Tbat the observed battery temperature, m a transfer coefficient, and epsilon white noise. In other words, the temperature in the urban canopy relates linearly to the temperature of the battery. Presumably there is some "resting" battery temperature, and so integrated over the entire domain
In other words, in general, batteries are anomolously warmed by the temperature of the boundary layer by heat conduction. Seems fair to me. While I sincerely doubt that error is white noise (there is absolutely a bias associated with the fact that cell phones are typically inside of something, be it a climate-controlled office or pocket), its an interesting use of modern proxies nonetheless.
Oceanographer, Mathemagician, and Interested Party