How can a phase be thermodynamically stable at room temperature if it only appears at high temperature?
$\alpha$-alumina is thermodynamically stable at room temperature, and also at high temperature (around $1,200-1,400 \space ^{\circ}C$) - however, alpha alumina is not what is typically formed when alumina is made from the various aluminum ores (ref). Typically, one of the several other crystal structures will form, with different particle sizes and amounts of water (hydration). These and all other phases that are found along the way to $\alpha$-alumina are called transition aluminas.

This link explains what happens upon heating. In general, first the crystal is dehydrated, which causes it to form a different, dehydrated phase. Then, as the temperature continues to rise, the alumina crystal structure rearranges into more compact structures, until eventually, near the sintering point, the atoms have sufficient kinetic energy that they can "find" the most thermodynamically stable configuration - $\alpha$-alumina.

In other words, the transition alumina phases are kinetically trapped in structures that are not the most thermodynamically stable, but heating allows them to get out of that trap and into the most favorable state.