Gaia was reported missing by her family from her home near Swanage in Dorset on 7 November last year.
She had not been seen for 11 days.
Family and friends launched a massive campaign to find the 19-year-old student, who suffered from severe epilepsy.
Two men aged 19 and 49, and a 71-year-old woman were arrested but released without charge.
Gaia’s body was found by police in undergrowth between Dancing Ledge and Anvil Point, close to the Swanage coastal path, on 18 November.
Her family said they wanted to know more about the circumstances of her death, saying she had been “really struggling” with a “lot of issues”.
The only family at the opening of the inquest at Bournemouth Town Hall were her cousin Marienna Pope-Weidemann and her mother Talia Pope.
“I am aware the family have a number of concerns in relation to Gaia’s death and some of those will be very relevant to my inquiry, but some will not be,” said Dorset Coroner Rachael Griffin
“It is not that I am unsympathetic to those concerns but they simply fall outside my remit.”
Coroner’s officer Andrew Lord said that pathologist Dr Russell Delaney was initially unable to establish a cause of death.
But after tests he was able to say that Miss Pope had died from hypothermia.
Mr Lord said she was formally identified by a “distinctive” tattoo on her body.
“Following the results of the post-mortem examination police have confirmed they are no longer treating the death as suspicious,” Mr Lord said.
Miss Griffin said she would be requesting statements from Miss Pope’s family, her GP, the Dorset Healthcare University NHS Foundation Trust, Dorset Police and Professor Matthew Walker, a neurologist from University College London who Miss Pope was under the care of.
“It has been brought to my attention that there are some concerns in relation to care provided by social services,” she said.
“I will request a statement from Dorset County Council in relation to that contact with Gaia.”
The coroner added that she would also want an entomology report to see whether the exact timing of Miss Pope’s death could be established.
The coroner adjourned the hearing until 14 May for a pre-inquest review and she had not fixed a date for the resumed inquest.
Gaia’s cousin, Marienna Pope-Weidemann, said after the hearing: “We know now what took her from us but when, how and why are all questions that must still be answered, not just for our sake but for the sake of the next family who wakes up in that nightmare some day.
“We are hopeful that the inquest will find those answers. The road is long but with your support we will get justice for Gaia.”