F13 indicates the dryer temperature sensor or dryer fan is faulty.
Unplug the appliance and take the top off.
Plug it back in.
Select the drying cycle.
Does the fan run?
The likely causes are the temperature sensor, broken wiring or a faulty main control board.
As you've renewed your repair plan you will covered for this.
The most likely cause is a temperature sensor.
However, if your repair plan is with Hotpoint, they can reprogramme the appliance from their laptops if it's a software fault.
Give them a call and they'll attend to the fault.
If you want to repair yourself, you would need to first test the wiring, then replace the sensor, if the fault then persists, it's the main electronics.
Hope this has been of some help
Let me know how it goes or if you need more help