The Valkyrie flew at Mach 3.1, close to the SR-71's operating speed in cruise. For the SR-71:
Fuselage panels were manufactured to fit only loosely with the aircraft on the ground. Proper alignment was achieved as the airframe heated up and expanded several inches. Because of this, and the lack of a fuel-sealing system that could handle the airframe's expansion at extreme temperatures, the aircraft leaked JP-7 fuel on the ground prior to takeoff. (Wikipedia; emphasis mine)
And if my memory serves me well, and if Discovery channel got it right, the SR-71 needed to meet with a tanker right away because of this leakage.
What was the Valkyrie's workaround/fix? The Valkyrie's Wikipedia article doesn't mention leakage prior to in-flight expansion.
I wanted to initially ask about the MiG-31's fuel tank seals, as the USSR developed heat-resistant rubber (and also special fuel like the SR-71 – the T-6) for that purpose, but since the MiG-31 is a lot cooler, it wouldn't have been comparable, though this piece of information might be relevant.
1: Wings of Russia TV documentary