Geologically, why is the middle east so rich in oil?

The region was a shallow sea (Tethys Sea) in a reasonably warm climate zone back a couple hundred million years ago or thereaouts, so there was a lot of plant life and algae that got buried, eventually turning into oil. Kind of the same reason that Texas has lots of oil (or had before it got taken out).

Everywhere that has oil, has that oil in sediments formed in relatively warm shallow seas at some past time within the past several hundred million years ago.

The Safaniya Field is the largest offshore oil field in the world and is located in the Persian Gulf. Because of the impact of the regional tectonic events hydrocarbon traps started to form.

Everywhere on Earth is "rich in oil." The oil in the Middle East is just closer to the surface than a lot of other places.

the heat must have something to do with it