That depends on the material. We see that for frequencies with the thermal occupation is very small. But there are frequencies that are very small, with k-vector close to zero. We also know that in that area the frequencies are linear in k. Therefore for low temperatures we ignore all optical branches and replace the frequency spectrum of the accoustical branches by where the speed of sound in the material is different for different polarizations and also depends on the direction of propagation.
Temperature is low when the approximation above is valid.