B777 Captain reported multiple EICAS messages resulted in expeditious handling and divert to a safe landing.

Narrative

At Cruise got EICAS message Aft Cargo Heat. Ran checklist. New EICAS message Bulk cargo Heat. Ran checklist. Then multiple new EICAS and Status messages and Flight Deck Temperature increased significantly. Ran checklists. SAT phoned Dispatch and included Maintenance Control and the Chief Pilot. Lost First Officers FMC. More EICAS and Status messages; it was getting confusing trying to figure out what was wrong. My biggest concerns were possible fire and that it was a cascading failure with an increasing volume of messages and problems as time passed. Maintenance Control helped us rule out a fire by determining that the flight deck temperature increase was an air conditioning problem. We had indications of lost fire detection; and left and center hydraulic system failures. And about 35 or more messages. The CRM going on was beyond my highest expectation. The support from my first officer and Relief Pilot was above and beyond. Support from Operations was it was spectacular the triple seven has such good systems and redundancy that even though we had many really bad indicators; all important systems were actually working flawlessly. The first officer flew the airplane and handled the radios. I talked on the phone and coordinated among the crew members. The Relief pilot made a PA and did a briefing with the purser. We requested priority handling and changed the destination to ZZZZ. We discussed the diversion guide and everything related to taking care of the crew and passengers with the Chief Pilot who coordinated it beautifully. Maintenance Control stayed busy reading the mountain of information that the plane was sending out. They did a fantastic job going over the highlights with us; giving best estimation of what the systems were actually doing as opposed to what systems were indicating. Troubleshooting the hydraulic system was very useful information. Dispatch provided Airport information; weather and landing data. We had about 90 minutes to deal with the problem and we left no stone unturned. We landed normally and were thermally; scanned and visually inspected by the ZZZ fire department. We taxi to a gate and waited about a half hour for customs to allow deplaning.