Date: 202102
Local time of day: 0601-1200
Location: ZZZ.ARTCC, US
Flight conditions: VMC
Light: Daylight
Aircraft: Falcon 50
Operator: Air Carrier
Operating under: Part 135
Flight plan: IFR
Mission: Passenger
Flight phase: Cruise
Airspace: Class A ZZZ
ATC / advisory: Center ZZZ
Aircraft component: Oil Temperature Indication
Component problem: Malfunctioning
Reporter organization: Air Carrier
Reporter function: Pilot Flying; Captain
Reporter qualification: Flight Crew Air Transport Pilot (ATP); Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine; Other Comm ASES
Anomaly: Aircraft Equipment Problem Critical
Detector: Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Provided Assistance; Flight Crew Diverted; Flight Crew Inflight Shutdown; Flight Crew Landed in Emergency Condition; General Flight Cancelled / Delayed; General Maintenance Action
Contributing factors: Aircraft
Primary problem: Aircraft

Narrative: We departed ZZZ on DATE at approximately Time LCL with two charter pax. All preflight checks were normal. We were fully topped off with fuel. As we were climbing through 26;000 ft I noticed that the number 2 oil temperature gauge was rising. I alerted the first officer (NAME) to consult the checklist and prepare for a possible engine fire or failure. There is no guidance in the checklist so we were left to use other resources such as each other; prior experience and MX techs in ZZZ1 through conversation via flight phone. We brought the number 2 engine back to idle power and noticed a brief reduction in oil temp. Within a minute or two the oil temperature gauge was at red line where it remained for the rest of the flight. We leveled off early at 33;000 ft. and made contact with Maintenance in ZZZ2. With the number 2 engine at idle we were able to maintain altitude at a speed of .68 Mach which was sufficient to troubleshoot the issue. I transferred control of the aircraft to the first officer and spoke with NAME1 (Maintenance tech). During the phone call we tried to find other indications that would lead us to confirm that the indication is accurate or erroneous. We did notice that the oil pressure did start to rise into the yellow arc when we advanced the power lever. However this could have been normal or unrelated. We took an SPR (snapshot) of the engine settings. We also reset the Oil 2 circuit breaker which isolates the oil 2 gauge for temp and pressure. The indication was as before... a red line temperature situation. We decided the best course of action was to shutdown the engine and divert to ZZZ3 as a landing could be made safely. Our Maintenance tech agreed. Given that a more serious condition could occur; such as an engine fire; failure or an engine damage/separation event we the crew elected to shutdown the number two engine and divert to ZZZ3. We performed the engine shutdown procedure then; due to the fact we were over Max landing gross weight and would require priority handling and would be landing at a high elevation airport without one of our three engines... I elected to declare an emergency. I declared with ZZZ center at 33;000 ft. and they gave us direct ZZZ3 and began our descent. We advised approach that we would require extended vectors to run through the applicable checklists and burn fuel for a safe approach climb in the event of a two engine go around. And to land below Max landing weight. The appropriate checklists were performed as a crew and the a visual approach and landing was executed uneventfully.We taxied to flight support where we shut down and began our company reporting process.




Synopsis: Captain reported a diversion and a precautionary emergency landing after a high oil temperature indication required an inflight shut down of the number two engine.