When starting my car the temperature gauge is past the red and the car is cold

So it appears the sensor is wrong or possibly a wiring issue. So let's go to the sensor and measure the voltage on each wire. You can do this in the vehicle or out of it. Basically if you do it out of the vehicle then you will want to put it in hot water and see if the voltage changes.

More than likely this is a coolant temp sensor issue but we should test it before replacing it however, they are cheap enough that you want to just go ahead and replace it.

Let me know if you have questions. Thanks