My g/f is truck is a 2000 Dodge Dakota 2.5L. This has happened a couple times recently but the cooling fan will stay on and not shut off until it drains the battery. We do live in Las Vegas so it is very hot, but the fan is staying on after we shut the truck off. The truck is not really over heating according to the temp gauge, but the truck was a bit low on coolant/water. I am thinking either there is a fault with the temperature sending unit or there is a relay sticking.. Has anyone had this problem or possibly know what could be causing this? The owner manual says nothing.

It sounds like you already narrowed down the problem.

Change the sensor and the relay and see what happens.

I'd try the relay first bec more then likely that vehicle uses a few of the exact same relays in it and if that does not fix it try changing the sensor.More then likely the relay is sticking and causing the fan to stay engaged or the sensors wires are shorting out or the sensor itself is internally faulty.

that is a relay causing that too happen,you can disconnect it and replace it,you might also want to replace the sending unit for it ,its not an expensive item to replace and it will assure you that the system is going to work right,i always replace both of those when l have to replace a relay it saves you from having future problems,good luck.