I have not noticed any temperature issues with my 6P, which I got just after launch. Are you using an application to monitor device temperature or are you noticing the device getting warm/hot when handling it?
Regarding the sudden drops in battery - does this result in the phone shutting down, or are you just seeing sudden drops in battery percentage along with associated negative spikes in the Battery screen? I'd have to guess that your battery is showing signs of wear. You could try using AccuBattery
https://play.google.com/store/apps/d...es.accubattery to characterize your battery health (it'll take a few days of charge/discharge to give you an accurate assessment).