The meter is running, and in a big way, on the money the state will have to pay the legal team for three Louisiana condemned murderers who successfully claimed the sweltering heat on death row violates their constitutional protection against cruel and unusual punishment.

The legal team initially asked Chief U.S. District Judge Brian Jackson, of Baton Rouge, in mid-2014 to order the state to pay the team nearly $775,000 in attorneys’ fees and costs.

But in September of this year, after the state’s attorneys alleged that some of the invoice entries were vague, duplicative or excessive, the judge ordered the inmates’ lawyers to meet with a special master in the case and reconstruct their invoice for fees and costs.

The prisoners’ attorneys did so, and on Monday submitted a new invoice. While it represents a 20 percent reduction in the total hours of work originally billed and a 50 percent reduction in travel time fees, it also included their work on the case from mid-July 2014 to Oct. 1 of this year.

The new invoice asks for $887,585 — or $795,550 in attorneys’ fees and $92,035 in costs.

In asking Jackson to award the new amount, Mercedes Montagnes, the prisoners’ lead attorney, wrote that they “take very seriously this Court’s care with the award of fees in this case” and had endeavored to provide as full documentation as possible.

A footnote to the latest filing by the inmates’ attorneys indicates that the lawyers were unable to obtain itemized receipts for their meals in order to separate alcohol costs.

“Therefore, Plaintiffs have reduced the total meal costs by 20%,” the footnote states. “Plaintiffs note that alcohol was only consumed at a fraction of the meals included in this request.”

Jackson has given the state’s attorneys until Dec. 2 to file a response to the new invoice. It will be up to the judge to determine how much money is awarded to the inmates’ lawyers. In his December 2013 ruling that found the state in violation of the inmates’ constitutional rights, Jackson said the prisoners’ lawyers would be entitled to attorneys’ fees. The ailing inmates filed their lawsuit in June 2013.

The inmates’ legal team, which has been representing the inmates on a contingent basis and have not been paid to date, includes seven lawyers and a dozen paralegals.

The state has recommended a daily cool shower, personal ice chests and more fans for Elzie Ball, Nathaniel Code and James Magee, the three inmates.

The case is currently on appeal.

Advocate staff writers Joe Gyan contributed to this article.