Air Carrier Captain reported a high speed rejected takeoff due to low hydraulic quantity warnings which resulted in overheated brakes; possible brake fire; and a tire deflating.

Narrative

During takeoff from ZZZZ Runway XXR in low speed regime; had a flicker of an EICAS Caution message R HYD QTY.The message disappeared instantly. Continued takeoff roll and through approximately 125-130 knots with a V1 speed of 166 knots the same EICAS caution message reappeared and remained and I made the decision to reject the takeoff. Immediate action items were followed and Tower was notified of rejection. I made the decision to roll to the end of the runway in hopes the brakes would be less likely to overheat considering in part aircraft weight /speed and runway length. We cleared runway at end and I stopped aircraft on parallel taxiway to complete checklists and assess brake conditions. The fire personnel had been notified and were proceeding to aircraft as we stopped on taxiway. I believe Tower personnel had made that notification to the fire personnel. We were in contact with Fire/ Rescue personnel commander on VHF 2. The brake temperatures eventually began to rise and the Fire/Rescue lead could see some smoke and at some point said possibly a flame; they sprayed water on wheel truck. This produced immediate results and temperatures were lowered and no further visible smoke or fire evidence. I did not feel evacuation was necessary and the Fire/Rescue lead agreed with that judgment as well as Copilot's. At some point Fire/Rescue advised the number 2 tire had deflated as a protection. Maintenance Control and ZZZZ Operations were all utilized. With the brake temperatures now at normal readings and in coordination with Fire Rescue and Operations the passengers were briefed on deplaning with airstairs onto buses and brought to terminal. Eventually the entire [crew] left the plane onto a bus. Operations/maintenance lead confirmed the aircraft would be towed for inspections.