When gas is compressed, it heats up. Moving rapidly through the air compresses the air in front, so it heats up.

It's as simple as that.

The ionization has nothing to do with it, though that probably reduces the heat slightly as it takes energy to ionize a gas.

Ionization actually reduces the effective temperature massively - from O(v^2) to O(v) at high (read: re-entry-like) velocities.