The mental image of it leaking so much fuel on the ground such that it needed immediate refuelling is a myth propagated extensively on the internet.
I had a quick search and found the KC135 chap who says the refuelling was needed due to leaks, but without being rude to him I'm not sure he's really a qualified source for that information. It sounds more to me like 2+2=5.
I'm procrastinating so lets do some napkin maths, the claim is
1) a significant amount of fuel is leaking out of the expansion gaps,
2) climbing up to 25,000 ft at 300 knots would heat the airframe enough to seal those gaps,
3) there would still be sufficient expansion room to allow for travelling at M3.2
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Ignoring that no engineer would be happy with 1.
For 2...Total Air Temp = Static Air Temp + Ram Rise. At 25,000 ft the static air temperature is about -35 C. Ram rise for a true airspeed of 300 kts:
RamRise = V^2 / 87^2 = 300^2 / 87^2 = 12 degrees.
So skin temperature at typical refuelling altitude would be -23 C
Titanium has an expansion coefficient of 9E-69 meters per meter-kelvin. So approximating rather grossly, assuming a s tarting temperature of 20 C over the 33 m length of the plane there would be a contraction of about 1 cm.
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And for 3:
The aircraft then accelerates up to 1900 knots. RamRise = 1900^2 / 87^2 = 470 degrees
Static air temp at over 60000 ft is roughly -55 C. So skin temperature would be 420 C. So assuming the same length and starting temp, the plane would expand by around 11 cm
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So to summarise: According to the claims, at ground level and temperature the expansion gaps were large enough to significantly leak fuel. After take-off the aircraft needs to be refuelled immediately. Assuming this is done so (i.e. take-off, climb to 20,000, refuel) then the skin temperature is lower than ground level, and the expansion gaps should have grown ever so slightly. The aircraft then climbs up to its M3.2 cruise point and everything expands significantly "as designed" and the gaps disappear.
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Perhaps the anecdote we'll see on the internet now is that the SR-71 had to take off and go supersonic to rapidly heat up the skin before briefly decelerating to refuel, but the refuel had to be done super fast to stop the skin cooling down too far...
From your source: "Fuselage panels were manufactured to fit only loosely on the ground. Proper alignment was achieved as the airframe heated up and expanded several inches.[30] 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."
If you dig past the internet comments and read some of the "primary source" books, the picture of the leaks is very different. I can't remember the exact book I read it in, but the author states there was a tank sealant, and it lasted around 50 hours (I think), before it needed to be replaced.
This is somewhat backed up by the Jenkins book [1] which talks about the time consuming process of replacing sealant, and the Graham book [0] that is the source for the Wikipedia claims on expansion. It talks of different sealants used, and how leaks were precisely noted and collected in _shallow_ drip trays.
[0] https://books.google.co.uk/books?id=dX5cCgAAQBAJ&pg=PA129&dq...
[1] https://books.google.co.uk/books?id=lEpWE748QUsC&q=sr71+seal...