I would like to know if it already exists (or maybe can be designed) a kind of protection against overcharge, overheating or burning because of such a (unknown quality) "replacement battery" ?

If I put such a battery (which may get on fire) in my phone, it may be interesting to have software check for internal phone heat, so that charging is turned off and maybe the complete device abruptly powered off.

Is it a stupid/naive idea ?