400 FSE will not idle when hot

[Gordonian]

Anyone any ideas about my hot idling problem. Tried the usual fresh fuel, new plug, cleaned the throttle body, had the injector professionally cleaned and tested. Con checked the engine sensors. All seemed ok. But still, after about 2-3 miles it starts cutting out at idle. Runs ok with throttle open. Does seem to get hot quite quickly. It starts easy enough and idles when cold. Starts fairly easily when hot but will cut out when throttle closed. Someone said coil pack but I'm not sure. Do you think I need to get the software and lead and go down that route?