The city’s Department of Correction is taking the heat following a judge’s determination that it has not been properly accommodating temperature-sensitive inmates.

Corrections officials had asked the court to terminate a series of “heat orders” issued over the past two years, which set up strict regulations governing the treatment of prisoners whose health is threatened by high temperatures. But a watchdog agency charged with monitoring city prison conditions claimed that less than a third of heat-sensitive inmates were being accommodated.

Since even basic record counts were in dispute, the judge chose to err on the safe side.

“Such an extreme disagreement over what should be a simple question — how many inmates were designated heat-sensitive — is reason enough to keep the Heat Orders in place,” Judge Harold Baer wrote.

The heat orders specify how long corrections officers can take to move vulnerable prisoners into air-conditioned rooms when the temperature exceeds 85 degrees. Compliance must be documented, and if a prison doesn’t follow the rules, it is fined up to $100 an hour to each inmate.

Since the corrections department seems to have made progress, Judge Baer wrote, termination of the heat orders might be appropriate next year.