Can elliptical galaxies be in a binary system or other form of relationship?
I don’t see why not. Most all galaxies are part of some cluster of galaxies, in orbits around each other. And clusters are part of super-clusters (or groups). The temperature of a galaxy would not have anything to do with it. It’s just depends on the relative velocities, distances, and masses of the galaxies. If they are going too fast (escape velocity), then even if they are close to each other, they are not orbiting each other. If they are going too slow, then they will eventually merge.