I had a similar experience on a 747 Classic some years ago.
Following heavy rain during the ground turnaround the subsequent departure and climb to cruise appeared normal, however upon making a step climb to FL370 we discovered the No3 T/Lever was immovable. We were able to accomplish the climb without difficulty and at the new cruise level the FCU provided substantially normal cruise thrust.
Suspecting ice build up had affected the T/lever control run, the TOD brief included a planned descent with the rogue engine at cruise thrust, managing any excess speed with speed brake, if the T/lever was still immovable at 10,000' the intent was to shut the engine down.
In the event it became necessary to shut the engine down and continue with an engine inop approach, the T/lever finally freed up at about 2,500'. It was quite interesting trying to manually handle the other three T/levers with the 'rogue' stuck in the cruise position.
After landing the engineers spent an hour chipping ice out of the No3 engine pylon, apparently the drain holes had somehow become blocked allowing the pylon to fill with water during the earlier turnaround which, then of course, froze on the subsequent climb out.