Neighbours rescued the woman from her home in Sorbie on Monday evening but she died at the scene.
Officers from Police Scotland's major investigation team are investigating the circumstances surrounding the fire and the death of Ms Stephenson.
A spokesman said they are treating the incident as unexplained, rather than suspicious.
Det Ch Insp Allan Burton, of the major investigation team, said: "We are currently carrying out our enquiries to establish the full circumstances surrounding this tragic event.
"We are keen to hear from anyone who may have had recent contact with the victim Mona Stephenson in the past few days, or indeed were in the area of St Johns Place in the early evening of Monday 26 January, to get in touch with us through 101 if they can help."
A joint investigation into the cause of the fire has been carried out by Police Scotland and the Scottish Fire and Rescue Service.
Police said the procurator fiscal has been informed and a post mortem examination is being arranged.
Police have named the 89-year-old woman who died in a house fire in Dumfries and Galloway as Mona Stephenson.