Phat is a backronym.
Sorry to disappoint everyone but the word 'phat' is almost certainly a derivative from the word 'fat'.
As early as 1951, calling something fat was a way of saying something was attractive or up-to-date. At some point afterwards, this mutated into phat , at least by 1963 where it was mentioned in Time magazine.
Emerging from the tradition of praise words, phat means 'cool', 'wicked' and is often applied to music (phat tunes!) or attractive women.
However, at some time in the 70's, people began to feel that 'phat' ought to have its own derivation. Perhaps they were uncomfortable with a praise-word like 'phat' should be associated with 'fat', which has negative connotations to a lot of people, particularly calling a girl 'phat'. Perhaps it was someone's idea of a joke and it proved compelling. I dunno. In any case, sources began to appear that claimed PHAT was an acronym for Pretty Hot And Tempting.
This meme caught on, strengthened because the acronym seemed to describe quite accurately the meaning of the word. Other bacronyms were developed later on, like PHiysically ATtractive. In fact, if loads of online dictionaries of slang have made the same mistake.
For more backronyms, fuck and posh are two words similarly mistreated.
http://www.ksu.edu/english/nelp/childlit/papers/355paper_2.html quoting the OED