First, a thought about chargers. I've tried many car chargers, new, used, dedicated car chargers, and plugs with USB connections. I still can't get a charger that keeps up with nav battery discharges. And yes, with each charger/charger-cable combination, I checked that the phone is charging AC. Some showed charging USB, and those were discarded or returned. But for all those saying you need a particular charger, if a charger is capable of charging other devices at over 3 amps, you'd think the "pipe" would be capable of delivering only 1 amp to my HTC. Next I'm trying a power inverter in the car with the factory charger/cable - I'll report results. But anyway...
Today I removed my HTC One from the Otterbox case before navigating. I was thinking maybe it would dissipate heat more efficiently, and allow the charger to keep up. Power Saver mode, no other apps running, and it discharged at a rate of about 1% every 5 minutes. That might be slightly better than being in the case, but if so, not much. However, when I put the uncased phone directly in front of an air conditioner vent, it stopped discharging. It didn't gain, but it didn't lose. I'll be ordering a vent mount, but that won't help much in January here in Nebraska.