Dorset Coroner Rachael Griffin opened the hearing into the death of the 19-year-old student at Bournemouth Town Hall.
The court heard that Miss Pope was reported missing by her family from her home near Swanage on November 7 last year.
The teenager, who suffered from severe epilepsy, had not been seen for 11 days and her disappearance prompted a massive campaign from family and friends to find her.
Her body was found by police search teams in undergrowth between Dancing Ledge and Anvil Point, close to the Swanage coastal path, on November 18.
During the police investigation three people, two men aged 19 and 49 and a 71-year-old woman, were arrested. They were released without any further action being taken.
Following her death, her family said they wanted to know more about the circumstances, saying she had been “really struggling” with a “lot of issues”.
The only family members present at the opening of the inquest were Miss Pope’s cousin Marienna Pope-Weidemann and her mother Talia Pope.
Miss Griffin told them: “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.
“It is not that I am unsympathetic to those concerns but they simply fall outside my remit.”
Coroner’s officer Andrew Lord told the coroner that pathologist Dr Russell Delaney was initially unable to establish a cause of death.
Following tests Dr Delaney was later able to say that Miss Pope, who was single and lived at Langton Matravers, had died from hypothermia.
Mr Lord said Miss Pope 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.
He confirmed to the coroner that the police did not believe there to be any third party involvement in her death.
Miss Griffin said that for the resumed inquest 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 May 14 for a pre-inquest review and she did not fix a date for the resumed inquest.
Speaking afterwards, Miss Pope-Weidemann said: “It was just a few days ago that the family received confirmation that Gaia died of hypothermia and our hearts broke all over again.
“Dealing with their shock and grief, Gaia’s parents, Natasha and Richard, and her sisters Clara and Maya, couldn’t be here today.
“But they wanted me to thank all our loved ones, whose loyalty and support keeps us going as we try to make sense of our sudden and terrible loss.
“Every minute without Gaia feels like an hour and every hour without answers seems endless.”
Miss Pope-Weidemann thanked the police, coastguard and members of the public who helped in the search for her cousin.
“Without the incredible grassroots efforts of our community, perhaps we would never have found her at all,” she said.
“Each one of you made a difference and we are grateful to know that still, we can count on your support.
“Despite everything she went through, she remained loving, joyful and brave. Here was a bright and powerful young woman who wanted to devote her life to others. We will always be proud of her.
“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 someday.
“We are hopeful that the inquest will find those answers. The road is long but with your support we will get justice for Gaia.”