I had this on one of my Ford cars in the late 80's I realise things have drastically changed but its worth a thought. Change the starter.
Same symptoms as yours and it was the field coil fault in the starter draining the battery but not pushing out power the other end to the flywheel to turn engine over when hot but worked fine like your s when cold.
Worth a shot in the dark be lucky.
Oh! your breakdown service is crap.
Bob
March 2014