Willie T was a bum.
Willie T's friends, The Professor, Ike, and Reggie were in an alley drinking. They were waiting for him to return with a bottle of whiskey. Instead, he ran past the drunken bums and said that someone was trying to kill him. The other bums just brushed him off, saying that it was just his imagination getting the best of him. The next day, they found his dead body in a refrigerator, facing inwards. The Police ignored their requests to reopen the case and claimed he simply died due to accidentially locking himself in a refrigerator and losing breath, but Monk got them to reopen the case when he realized a telltale clue that would prove otherwise: only one handprint was visible, and had he actually been locked in, accidentially or deliberately, he would have been clawing around. The coroner then changed his cause of death to being strangulated, presumably with a plastic bag.
He was murdered because he saw Owen McKlusky painting a drawing of a fountain on Leland Stottlemeyer's door, which would expose his conspiracy. Interestingly, in the flashback, it was shown that he was carrying a gun, even though that wasn't the murder weapon. (Monk: "Mr. Monk and The Miracle")