Mine is in a plastic casing with no apparent heatsinks, externally at least. It has six LEDs marked from 1A up to 6.
Tricky for me, since the car is in a very exposed paved area at the front of my house. I don't suppose anyone would take advantage and stroll off with the charger but I'd rather not leave the car with the bonnet unlocked and cracked open overnight. But from what others have said, it might be worth trying the starter after a few hours.