The correct answer is C) Shutdown the engine. If the lube oil supply temperature continues to rise after reducing power to a gas turbine engine, this indicates a more serious issue that requires immediate action to prevent further damage. Shutting down the engine is the appropriate next step, as continuing to operate the engine under these conditions could lead to catastrophic failure. The other options are not the best course of action in this scenario. Checking oil consumption (A) or further reducing power (B) may not address the underlying problem, and a water wash (D) would not be an immediate solution to the high lube oil temperature. Shutting down the engine is the safest and most prudent action to take to prevent potential engine damage or failure.