Intermittent non start of Punto 2003 ?

Fiat Punto 2003 1249cc petrol.
Over last 6 years intermittentlly the car does not start.
Normally in hot weather after been left in sun all day.
It turns over well. battery new.
Can be started every time by bump starting it or putting it in gear and trying to start a few times so the car moves, then it will start.
Fiat have tested it twice and can not find a fault, like other people as fault never on when they investigate.
I have recently been told , it must be the wiring of the starter motor? The problem getting worse so help badly needed.