Well, I'm a psychologist by training, but not a clinician so I could be way off. That said, is believing their hands will catch on fire the only sympton of disordered thinking that this person shows? Does it interfere with their ability to get on with life (hold a job, that sort of thing)? Is it a belief that they'll catch on fire only if they do something in particular (e.g. if I don't wet them every hour)?
For a true diagnosis, there are almost always other symptons of disordered thinking involved, nothing appears in isolation. Depending on the answers to the above and other issues, I could see a few possibilities: schizophrenia, OCD, generalized anxiety disorders, etc. If it doesn't interfere with their life in any significant way though, it's hard to really give a diagnosis because that's usually one of the criteria too. Of course, I could totally see a regular but unscrupulous MD (not a psychiatrist) just prescribing some anti-anxiety meds for it w/o sending the patient to someone qualified to judge.
Hope that helps! My knowledge of this stuff fades ever more each year that I'm not doing psych, so maybe someone with better qualifications can help.