My understanding is that it will try, it just won't succeed. It'll keep the adapter at its extreme limit. You're quite right that the adapter shouldn't fail at its own limit, but nothing's perfect and if there are any flaws that's when they'll show up.
Just a quick note... I don't want terms to be misleading/confused:
- A charger is a device that you put your removable batteries into.
- An adapter is a power convertor that you plug in the wall, then plug in your device to charge the internal batteries.
What we've been talking about have been adapters, and NOT chargers.
So with that said:
Just to provide correct info, depending who might have told you this, simply said, an adapter won't "try" anything.. it's not a bidirectional thing.. the charging circuits of the device take whatever they get from the adapter and make the most of it, while the adapter is just converting the amount of power that it's been built for. A decent adapter will have protection circuits to prevent overloads/overheats (basically to prevent frying should there be a power spike in your wall socket, but nothing towards the device that's pulling from it).
Unless it's got an adaptive capacitor or a very fancy computerized device and not just an adapter, a 0.5A adapter is going to be putting out 0.5A at all times, no more, no less, same with 1A, and 2A adapters. It's the device that manages this power input that has a circuit that cuts out the "excess" incoming power. This is done to prevent overloading the charging circuits that are internal to the device and the battery's recommended max. charging capacity.
Yes, if the higher amp charging is heating it up. I've never had any of my internal battery devices heat up noticeably while charging at the recommended rate, so it isn't likely that it's doing them any particular harm. The Cool Fire could be different, of course, but I wouldn't expect it.
You'll notice a much larger difference if your device (a tablet for example) is almost dead and you put it on its adapter that pushes the max it can handle... give it about 15-30 minutes then touch the back, you'll feel the battery being much warmer than usual.
Note that the charging circuit on just about all device will start turning the incoming power down when it senses/registers that the battery is at 90-95% fully charge and then trickle charge the rest, so to 1) allow the battery to cool, 2) topping off any battery to reach 100% of it's capacity can only be done properly with a slow charge rate.
That's why you see some fairly extreme chargers that "can recharge your battery to 80% in just a 1/2 hour (but then takes another 1-2 hours to do that last 20%)". Those chargers are pushing those batteries hard as heck to force it to gobble as much power as possible within the safety limit of the battery's capacity. No question about it, those batteries aren't going to last from being stressed that hard.
Note that if you could have a special adapter that has been built with the device in mind if the batteries are non-removable, while if it's an external charger, that circuitry that controls the power going to the batteries in built-in that charger... these are different from standard power adapters that you can plug anything into.
Personally, I'd never use such charger, I'd rather have 2-3 spare set of batteries that are being slow charged.
And out of my several mods, single or dual batteries, I've charged them all regularly via the USB and never had any trouble... and that's for the last 2+ years (and add to that another several mods that my wife and daughter's have and also only charge via USB). I use my external charger more for the spare batteries, and whenever I've tested the USB charged batteries, they always measure out the same as they would with the charger, so I have absolutely no worries about using the USB ports of my mods.