Pol Col Ekarat Intasueb, chief of Mae Sot police station, said Muller was found with a rope tied around his genitals and waist and another rope tied around his neck, hanging from a knob of his bedroom door.
He said there was no sign that the American had been assaulted.
Equipment for injecting crystal methamphetamine, five methamphetamine pills and several sex toys were also found in the room.
Muller appeared to have died from asphyxiation or from a heart attack after a drug overdose, police said. His body had started decomposing and giving off a bad odour. Police suspect he had been dead about three days when his body was found. It was sent to Mae Sot hospital for a post-mortem examination.