In shrinking, the temperature goes up, which leads to gravothermal catastrophe. Binary stars are primordial formed at the birth of the two stars. In a three-body encounter, one of the stars is ejected, carrying away with it energy. In a two-body encounter, energy is lost via tidal dissipation. There are soft binaries that are easily disrupted.
Soft binaries get softer.
There are also hard binaries. Heating the center of the globular cluster puts energy back into it, and it expands. When it expands, the temperature goes down. To ascertain this, a high-resolution telescope is needed. M-15, one of the densest globular clusters known.