I'm surprised (or overlooked) there wasn't a check for clustering of data. One set should clump close (with 24/7 consistency) to normal indoor temperature, while another should clump (with greater spread and time-of-day variation) around actual outdoor temperature. Split the discernibly HVAC-skewed values out, and you'll get a better grasp on the actual outdoor temperature. You could then sub-split the latter into warm-body proximity clustering (phones in pocket vs. otherwise).
My guess is that's accounted for in each city by the m and k values. Note that these values are essentially averaging the battery-temp-affecting behavior of everybody in a given location (as well as the local temperature variations as well) and mapping them to the "official" temperature (usually measured at the airport). That makes the whole exercise rather useless in my opinion: it doesn't provide more information than a weather report, just a vague redundancy. Significantly, they will never be able to isolate all the factors so that a single phone can tell you the local air temperature.
As Dylan famously said: "You don't need a weatherman to know which way the wind blows."[1]
