Is it possible for a crystal to have different structures at different temperatures?

For instance, suppose it is a 50-50 alloy of two metals that is BCC at room temperature $T_0$. If I raise (or lower) the temperature, is it possible for the bonds in the crystal to rearrange and form a new structure (say, FCC) that is more energetically favourable at the new $T$?

I saw a question on an engineering forum (here) that seemed to suggest the only thing that affected the structure was the % composition of the alloy. Could temperature play a role, too?

Answer

The microstructure of an alloy depends on such variables as the alloying elements present, their concentrations, and the heat treatment of the alloy (i.e., the temperature, the heating time at temperature, and the rate of cooling to room temperature). -Materials Science and Engineering: An Introduction 9th, Wiley, Calister, Rethwisch

Look up phase diagrams for different alloys

Here is a phase diagram for iron and carbon (steel). Depending on the composition of the alloy and the temperature it is at different crystal structures will form and multiple phases can be present at the same time. $\alpha$ is ferrite and has BCC structure, austenite ($\gamma$) has FCC.