What OpenAI models support thinking, custom temperature, or both?

I ran a quick check against OpenAI models released in the last six months. “Thinking” here means the model accepted reasoning.effort; “custom temperature” means it accepted a non-default temperature parameter in the test.

What’s interesting to me is the number of models where it appears inconsistent. I wonder why this is?

Why does 5.5 NOT support custom temperature, but 5.4 does?