The original question was on rotation from a rig take off, hence normally no obstructions as the sea is relatively flat. Thus the priority SURELY must be to fly the aircraft (using automatics or mandraulic) then once going up fight the fire.
One thought about a hot gas leak, we pause at each movement of the SSL to confirm signs of fire and to diagnose if it is a hot gas leak. If the warning goes out at idle then likely a hot gas leak, but what now? A wise TRE suggested to me that a hot gas leak @ a couple of hundred degrees C can still cause a fire so shut it down anyway. I believe in his outlook and would rather recover one engine with much less fire hazards than to keep it going and risk further fire. This of course means you cannot restart the engine if it does indeed have a hot gas leak so it's time for a single engine landing. Not your day if that all becomes a problem.
Si