The Intake Air Temperature sensor is basically a thermistor, i.e. a resistor that increases resistance with temperature. The ECU sends 5 volts to the sensor, and expects much less than 5 volts back. If it sees 5 volts, or close to it, coming back it gives a P0113 error. If it was seeing no volts or low volts you'd be getting a P0112 error, so it's not a connection problem to the sensor itself, instead there's more likely a short in the wiring or the ECU itself which is returning the full current back to the ECU.
The places this could be happening are:
- The IAT sensor connector
- The wiring between the ECU and the IAT sensor connector: this is most likely to be the cause
- The ECU itself: least likely. If it is the ECU you'll probably need to send it away or replace it unless you are really good with electronics and have the right tools
I would start at the IAT sensor connector and work my way back to the ECU, looking for frayed wiring. If you have a multimeter you could use that to check for 5 volts at the connector as well. Once you have located the source of the problem assess it, you may be able to resolve it by insulating the wires from each other if they aren't too damaged. If the wiring is badly damaged you'll need to replace that section of wiring.
- Find out what caused the damage to the wires (heat, friction, etc.) and take steps to make sure it doesn't happen again by re-routing or securing the wires once fixed
- Keep in mind whatever damaged the IAT wires may have damaged others, or could damage them in the future, so inspect other wiring too