Where is the fuel regulator located and how to check it on a 05 Tuson..?

Hello, To check fuel pressure, use a fuel pressure gauge at the fuel rail. If your rail pressure is low, you will want to check fuel line pressure. Since the issue goes away as the engine cools down, I would not expect fuel pressure to be the issue, instead, I would start by scanning for trouble codes that are stored or pending, especially if the check engine light is on. Do you have stored or pending trouble codes?