QuickCharge 2.0 allows up to 3A at the standard 5V, and if you plug it into a phone that doesn't support QuickCharge 2.0, no harm done - the device will draw what it wants and it just means 3A are available to draw, which most devices will not use.
If your phone supports QuickCharge 2.0, the device being charged can also ask for the voltage to be stepped up to 9V or 12V. If your phone doesn't know how to ask for more voltage, the voltage stays at 5V.
If the phone is QC2.0 compliant, it will ask for more voltage, and if your charger is QC2.0, it will provide it. It makes no difference whether the QuickCharge was made my Motorola, Samsung, or anyone reputable. QuickCharge 2.0 is QC 2.0. It's a standard. You might have poorer results if you buy the $2 "Magical Sparkles Fastly Charging for All Batterie" off "SparkySparkyBoomBoom Battery Blowout Direct", of course.
You are seeing elevated temperatures because that's what happens when you try to change battery chemistry rapidly. It's an exothermic reaction with Lithium batteries, and it will reduce the effective life of the battery. So has rapid charging of current Lithium technology always been. Charge it fast, plan on replacing it a little sooner. Charge it slow, it lasts longer, but you have the inconvenience of waiting bloody ages for it to charge each time.
Most phones that implement QuickCharge 2.0 only use the higher voltage for fast charging an almost empty battery, because that's where rapid chemistry changes do the least harm. "Least" harm does not mean "no" harm. It will start at 12V@3A because it can dump a shedload of juice into an empty battery that way and still keep the temps down to the point where there's no significant damage. Then it'll drop to 9V@3A for a while, and then finally finish off the last 20-25% of charge at 5V@<3A because that's where the battery is already accumulating the most damage even from a normal charge, and accelerating that part is a really bad idea.
EDIT: If you use fast charging twice a day to get your battery from 30% to 60%, you'll probably accumulate about the same amount of damage as if you used regular charging once a day to get the battery from 10% to 100% then left it on trickle charge all night. Lithium is stressed as much by sitting at its voltage extremes as it is by rapid chemistry changes. So if you find it more convenient to plug it in to Fast Charge when you get to work, let it amp up to 60-70%, then boost it again at the end of the work day so you don't have to plug it in overnight, in all likelihood it's going to work out to about the same as trickle-charging it all night.
Slow-charging it to 60% twice a day is even better for the battery, but ain't nobody got time for that.