It sounds to me like you are describing a rare condition known as Congenital Insensitivity to Pain with Anhidrosis (CIPA). This is a severe type of autonomic neuropathy (nervous system disorder). There are some other forms that are less severe as well. Currently, there are about 40 reported cases in the US. CIPA is typically diagnosed a few months after birth and there is now a genetic test for it - the most severe forms of CIPA are linked to mutations in a gene called NTRK1, which encodes a protein necessary for normal autonomic nervous system function. However, there may be other genetic links and, even in the case of NTRK1, no one really understands why the person is unable to feel pain.

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