The large J2 limit of the square-lattice J1-J2 Heisenberg antiferromagnet is a classic example of order by disorder where quantum fluctuations select a collinear ground state. Here, we use series expansion methods and a mean-field spin-wave theory to study the excitation spectra in this phase and look for a finite-temperature Ising-like transition, corresponding to a broken symmetry of the square lattice, as first proposed by Chandra et al. [Phys. Rev. Lett. 64, 88 (1990)]]. We find that the spectra reveal the symmetries of the ordered phase. However, we do not find evidence for a finite-T transition. We suggest a scenario for a T=0 transition based on quantum fluctuations.