Thanks Javal that explains why it starts when cold but not hot. Though the big thing that leads me to think it is the battery is with a "booster" pack the starter motor works.
i'd be getting an amp clamp over the main starter wire and seeing what the draw is whilst holding a multimeter on across the battery terminals to make sure it doesn't drop below 10v at up to the value of the CCA of the battery.
If the amperage draw is > 300 odd, I'd suspect the starter is faulty when hot.