Another inmate, Donnell Murray, would later recall in a message to his fiancée, “The fire alarm was sounding off and I could smell the smoke, and we were immediately locked in our cells.”

Then, the jail went quiet.

The Bureau of Prisons said Mr. Quay adequately notified Washington about the “initial fire and subsequent events.” The bureau did not say when this was done and what it did in response.

Many inmates said that after the fire, the lights went out and they were locked in their cells for up to 23 hours a day, a lockdown typically enforced in emergencies, to keep staff safe. Asked how many days he was locked in, an inmate on the fourth floor later said he believed three consecutive days passed before he was released again, but he had become confused in his dark cell.

“I had no idea what time, what day — you lost track of everything,” the man, who asked that his name not be used for fear of reprisals, said in a phone interview.

Cold air blew from a vent over his bunk. He tried to block it with a book cover. He lay listening to a battery-powered radio, wrapped up in three blankets, he said, until a guard saw he had an extra blanket and took it away.

Still, he worried more about his cellmate, who suffers seizures and was not given his usual medication. The jail’s computers, used to request prescription refills, were down, along with the monitored phone system inmates use to call family. A line that connects the jail to local federal defenders’ offices was working, though, and when they were briefly released, the inmates began to call the lawyers.

“They sound really frightened,” said Deirdre von Dornum, who leads the Brooklyn office of the federal defenders, on Jan. 31. She said the number of calls peaked that day, when temperatures fell to 2 degrees.