The doors were from years ago and remember they unlocked them for the tourists. The tourists are another another reason that the furnace is still on.

Perhaps the first time he found the door hard to open and went through the flames
But rather than this being a plot hole, why isn't anyone discussing on how easy the doors are to open? How the cell doors locks are so easy to open?
After all, if the Rock had been closed for 20 years, those metal doors would have been rusted shut
And why, if the Rock has been closed for 20 years, why is that furnace still burning? What is the need for it? And how is it getting fuel?

Perhaps first time round the doors he swings open for the marines were firmly locked, so he had to come through the flames. This time he took lockpicks and his prison skills , but they were unlocked it turned out.

This is one of the plot holes that has been discussed here. Great observation.