Warshaw said Saturday that authorities were still working to determine what sparked the incident, adding it wasn't clear how much time had lapsed between the time Cresci was killed and when the fire began.
Authorities have said Cresci could have been dead for several days.
His longtime friend, Scott Broschart, told the Asbury Park Press of Neptune that no one had heard from him since last Sunday.
Broschart, who said he was helping Cresci open a restaurant, said his friend and Schlesinger had been dating for about 18 months, and that they "had their up and down moments."
Cresci's father, Victor, told The New York Post that Schlesinger "was mentally ill, and Daniel wanted to help her," despite his family's warnings that she appeared unstable.
Schlesinger, who also owned and operated the New Jersey State Dog School in Holmdel, made headlines in May 2004 when she was attacked in Central Park while walking her then 4-year-old, 48-pound Shepherd mix, Cookie.
The assailant, Tito Rodriguez, grabbed Schlesinger by the hair, tore her shirt and ordered her to perform a sex act on him, but she and her dog fought back.
DNA tests conducted on the blood drawn by Cookie's bites eventually led investigators to Rodriguez, who was convicted of assault, attempted rape and sexual abuse . He was sentenced in 2005 to 125 years to life in prison.