Mac Austen, when he had a water-way leak, blocked off the supply to the rear bearing on his PRM gearbox - reckoning he would have to get a new box in any case.
It served OK for about 3 seasons, then had to be replaced.
Yes the cooling is important, but loss of it does not produce an immediate breakdown.
The handbook for the PRM gearboxes specifically states that water cooling must be used. They are hydraulic gearboxes and if the oil gets too hot then there may be no drive.
It may be that they will function without a cooler but I doubt that they would work very long at higher loads.
I have found the PRM people on the LBS stand to be most helpful and knowledgable even giving advice and assistance on products long out of production. They also pointed me towards companies who would be able to give more info on older gearboxes.