How do we explain the healing of some medical conditions—such as infertility or severe wounds—after visiting charlatans who perform extraordinary feats like drinking hot water or extinguishing a heated knife with their tongue, in order to refute those who use this as proof of the charlatans' abilities?

Healing at the hands of charlatans does not permit approaching them or seeking treatment from them, because devils participate with them in this to entrap people into shirk (definition) (polytheism). Abdullah ibn Mas'ud, may Allah be pleased with him, clarified that what devils do, such as inflicting pain and then ceasing when a charlatan performs ruqyah (definition) (exorcism), is merely the work of the devil. True healing is that which comes through supplication to Allah alone. Dr. Musa Al-Zahrani also mentioned that the supernatural occurrences of people of shirk and bid'ah (innovation), such as healing the sick, come from the devil who inflicts harm and then removes his harm when they deal with the polytheist and the innovator.