Look, let me put to bed the tyre failure/overheat/fire scenario.
The 777 is fitted with:
1/ TPIS, which stands for "Tyre pressure indicating system" which is monitored by EICAS, the crew WILL get a message if a tyre deflates. If they suffered a major tyre failure on takeoff they would have felt the problem ( especially if it was a nose wheel tyre ) and then received an EICAS message.
2/ if there was a Wheel Fire in the main Wheel Well they would get a EICAS Fire Wheel Well Warning and they would have followed the QRH procedure and then declared a Pan or Mayday as required. This would certainly NOT include climbing to FL450 to put out the Fire!!!
( the QRH from memory says to slow below MLO .82/270kias and extend the gear, if the warning continues LAND ASAP. )
I've had tyres deflate on T/O at MTOW on a 77W out of LAX, no big deal. We had a slow deflation and nothing found on the runway, we continued. Tyre was flat on landing.