CL-350 flight crew reported a hydraulic system malfunction during initial climb resulting in a diversion. Flaps were also inoperative during approach.

Narrative

Departed ZZZ on a Challenger 350; at approximately XA:30. With X passengers and 2 crew.We Departed Runway XX with an initial climb to 3;000 feet. Weather out of ZZZ was 160@7 overcast 400. Upon reaching flap retraction altitude; the flaps were commanded stowed and the after takeoff checklist accomplished. Within seconds we received a R HYD TEMP HIGH" amber CAS message. We verified on the hydraulic synoptic page the temperature which at the time was well over 100°C. The PIC called for the applicable QRH; and ATC was notified we would be stopping the climb at 7;000. As I began to follow the QRH; the Temperature spiked to 200°C. It was at this time the QRH called for the Right engine to be shut down. The Temperature never remained constant; but fluctuated between 180-200°C erratically. Before shutting the engine down; we transferred controls and the PIC confirmed all steps in the QRH prior to this point had been accomplished. I assumed positive control of the aircraft as well as the radios. I [requested priority handling] with ATC and asked for vectors to ZZZ1. The decision to head towards ZZZ1 had there been any issues after takeoff was briefed and communicated on the ground beforehand as part of the take off briefing. Upon completion of the QRH; controls were switched and the PIC was given control of the aircraft. We briefed the weather in ZZZ1 (overcast 1;000 winds 180@13); the box was set up for the ILS XYL; and services were coordinated. The PIC also briefed the passengers on what was happening and what to expect. We completed all applicable QRC checklists and items. We determined that we would be overweight by a little under 300 lbs. Once cleared for the ILS XYL we began to configure and were switched over to ZZZ1 Tower. The PIC called for flaps 10° and flaps 10° was selected. We had a no flaps indication on the display. Subsequently we had multiple amber CAS messages 'Flaps fault' 'flaps Fai' 'Flaps Norm Pressure Low'. 'Spoilers Fail' The decision was made to execute a Go around. We alerted Tower of our intentions and were given a heading and vector away from the airport. The decision was made to leave the gear down and keep the speed at 200kts. Once at a safe altitude and cleaned up from the Go Around the 'Flaps Fail' 'Flaps Fault' 'Flaps Norm Pressure Low' and 'Spoilers Fail' QRH was ran. Every line item was completed and resulted in no flaps being indicated. As a crew we determined we would be executing a single engine no flaps landing. Per notifying ATC of the new issue the recommendation of ATC was to switch to [Runway] XZR as it has a longer length. We immediately determined this would be the best course of action being our ref speed would be in excess of 150 kts. We were given vectors while configuring the box for XZR. XZR was briefed; and ATC notified that hydraulic braking may or may not be an issue and we may need to be towed off the Runway. The applicable QRC items were accomplished the passengers briefed once again that this would be a longer than usual landing. The PIC and myself also discussed the handling characteristics of the aircraft should the spoilers not deploy on landing. It was briefed that I would manually deploy them had I gotten an indication they were not deployed. Upon landing on XZR; the spoilers were manually deployed and we were able to exit on Taxi way 1. We requested that ARFF (Airport Rescue and Firefighting) take a look at the airplane and if no visible signs of damage or fluid leaking were seen we would taxi to signature FBO under our own power. None were noted. Upon taxiing to the FBO and the remaining engine shutdown; passengers were de-briefed on event and as a crew we made sure there needs were attended to. The PIC then made the appropriate calls to the company."