it could well be the starter , i may need a software update as well. if the starter doesn't reach a certain rpm when turning over the car wont start .you can get the ecu software modified for this or you could just replace the starter motor .
car starts easier when warm as it doesnt need to crank over as much to start .
have you checked the battery ? maybe it has a cell going down. this would lower the cranking power when cold ,but would start easier when warm as the battery will have more charge .