Well, I'm not sure about maximum amplitude of vibration. It is possible to calculate average energy per atom and thus average amplitude of vibration.
Einstein used a simplified model, in which each atom represents three harmonic oscillators (for the three dimensions). All the oscillators are considered independent. This independence can't be correct of course, but the model still gives rather good predictions, except for very low temperatures. The average energy (that is per atom, per dimension) turns out to be:
\frac{1}{2}\hbar\omega+\frac{\hbar\omega}{e^{\frac{\hbar\omega}{kT}}-1}
Debye improved on this model by taking into account that the oscillators affect each other. Now oscillation of any of the atoms will propagate through the whole thing. Debye made some clever assumptions which allowed him to solve the equations that arise in this situation. His result for the average energy (again per atom, per dimension) was
\frac{3}{8}\hbar\omega_D+\frac{3\hbar}{\omega_D^3}\int_0^{\omega_D}\frac{\omega^3}{e^{\frac{\hbar\omega}{kT}}-1}
with
\omega_D^3=6\pi^2\frac{N}{V}\overline{v}^3.
\overline{v} is the average velocity of the propagating waves in the crystal, N the number of atoms and V the volume.
As you may notice Debye's method is a little harder to use. So, when you're not dealing with very low temperatures, you might as well use Einstein's results. I'll leave it to you to calculate the amplitude from these results.
Also, see http://en.wikipedia.org/wiki/Debye_model" for some more information about both models.
