Dear Layth, here is a Journal of Applied Physics article specifically on grain growth in polycrystalline Germanium, by H. Atwater, C.V. Thompson, & H. Smith from MIT, comparing thermally inducing grain growth with ion induced grain growth.
I attach the paper as well as a key graph in Fig.7 showing the temperature dependence of the grain growth rate in polycrystalline Ge.
Generally, grain size increases with annealing provided temperature is sufficient to move grain boundaries. In case of germanium, I think annealing at 200 C should not affect its grain size.
Yes, the grain size increases with increasing the annealing temperature. This is because increasing the annealing temp. leads to increase the crystallinity of the material and hence increases the number of crystallites.