-20°C is the limit of the CR2032 battery. If you install a BR2032 battery it should then read down to -30°C.
There's talk, but no confirmation or denial from G as yet , that the Tempe is recording full 24hr temperature data on a rolling 365 day period, and that it only requires a firmware update on selective Garmin head units to access this data. Whether this is true or not remains to be seen, but for me working in microelectronics, I cannot see why not as this feature wouldn't require much in terms of storage to accomplish.
Precision wise - when it comes to accuracy of the Tempe device I've checked my product against a reference thermometer and it read within 0.3°C@0C/0.4°C@20°C. Transient time (0°C-20°C) was noted at a mean 13 minutes. The Edge 800, for reference, measured 21.
My best,
CofTQLT