When the unit is within the 32 °F and 113 °F temperature range, the external power source will power the unit and charge the battery. The unit's charger will always provide 100% to the unit and send any extra power to charge the battery.
As a preventative measure do not leave your device in direct sunlight. By keeping the device out of direct sunlight the unit is more likely to charge when getting into a hot vehicle.
The best thing to do if your device is not powering on in the vehicle, or your battery is only lasting 30 minutes is to charge the unit overnight by using either an AC adapter (not included in most of the units) or USB Cable attached to a computer. Charging from a USB cable connected to a computer will charge the unit at 30-50% of the rate of which it would charge if plugged into a 12-volt vehicle power cable.