Kerryn Tate was last seen alive on December 29, 1979 when a friend dropped her off at her Perth home after a surf club party.
Western Australian police believe the 22-year-old intended to travel to the southern suburb of Karragullen later that day to house-sit for friends.
"Sadly she never got there," Detective Senior Sergeant Steve Potter said on Wednesday.
Her charred body was found in dense bushland on the city's outskirts not far from the Karragullen home about 24 hours later.
A fire had swept through the area after Ms Tate's body was dumped about 800m from the Brookton Highway.
Despite this, crime scene officers recovered evidence that has recently resulted in the identification of an unknown male DNA profile.
Detectives are trying to track down the man and have appealed for anyone with information to come forward.
"Somebody in our community knows what happened to Kerryn," Det Potter said.
He also said it was possible the fire could have been lit to destroy evidence.
"Fire had gone through there but that's not what caused her injuries," he said.
Ms Tate's family remains deeply affected by her death.
"Although many years have passed since Kerryn's murders, just hearing her name or seeing her face still brings us to our knees and breaks our hearts again," they said in a statement read by Det Potter said.
Ms Tate had been living in WA for about a year having left her home in NSW.
She worked in the arts and was known to often hitchhike. She was described at the time as a social woman with many friends.
Det Potter rejected a theory Ms Tate's death could have been linked to witchcraft that was prominent in the years after her body was discovered.
A $1 million reward has been offered for information that leads to the apprehension of the person or people responsible for Ms Tate's death.
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