Semiconducting materials have relatively small band gaps, they are insulators that take very little additional energy to become conductors. In contrast good insulators incinerate before they start conducting (or turn into plasma).

Energy being energy means that high enough ambient heat can kick electrons into the higher orbitals because the band gap is so small. This also happens at normal ambient temperatures, but those electrons don’t make it very far and there aren’t that many. At 200c a closed gate is not stopping enough electrons from moving through it anymore.

At least this is the slightly hand waved technical explanation. Project in Flight on Youtube has an excellent video on how semiconductors work.