The cause of the blaze, which broke out early on Wednesday at the 11-story Anson House in Thornaby-on-Tees, is being investigated.
Police said they were also trying to piece together her whereabouts in the run-up to the fire.
Ms Bolam was described by her brother, Malcolm, as "a loving sister" who would be "greatly missed".
Det Insp Matt Hollingsworth, from Cleveland Police, said: "Our thoughts and sympathies are with Teresa's family.
"It's extremely important that we are able to pinpoint the cause of the fire, and whilst there is no current suggestion that Teresa died as a result of criminality, we do need to piece together her whereabouts as part of the investigation.
"I'm appealing for anyone who may have seen Teresa in the days prior to her death to contact me."
A woman who died in a fire at a Teesside tower block has been named as Teresa Bolam.