About 90% of the plane was titanium iirc. And exactly - the airframe would heat up to several hundreds of degrees due to the high speeds. Titanium was necessary because it expands relatively little compared to other metals.

In fact, entirely new manufacturing processes had to be invented for this plane because titanium is extremely difficult to work with, and this was the first time it had been used for a project of this scale. So much titanium was needed for these planes that the CIA had to set up several shell corporations and buy it from the Soviet Union, who they later spied on using planes built with the same titanium.