Vikki Thompson, 21, of Neville Street, Keighley, died at Armley jail on 13 November. She had said she would kill herself if sent to a male prison.
She was in custody awaiting sentencing for robbery and was being held in a single-occupancy cell at HMP Leeds.
Wakefield Coroner's Court was told staff had been checking her hourly.
Updates on this story and more from around West Yorkshire.
When she was checked at 19:00 GMT, Ms Thompson was seen to be lying on her bed, giving no cause for concern, the inquest heard.
But when she was checked again at 20:10 she could not be seen and staff went into Ms Thompson's cell.
Emergency services were called and she was pronounced dead 38 minutes later.
A post-mortem examination found the cause of death was thought to be hanging.
The inquest was adjourned for police and Prison Service investigations. It will be heard by a jury at a later date.
Ms Thompson's body has been released to her family for cremation.
Her death has prompted calls for a shake-up of the government's handling of transgender prisoners and a change in policy.
A transgender woman who was found dead at a male prison was considered to be "at risk of self-harm", an inquest has heard.