When I shut the car off it leaks coolant. The hotter the engine is when I turn it off, the more coolant leaks out. So, it sounds like the overflow. Do the overflow container/battery trays have a history of leaking?

 

Watch it when it does it and see where it is coming from. If there is a leak it will run out if you have the overflow filled up. If it is filling up and overflowing it might be some problem or you have to much coolant in there. I think you fill it when the car is warmed up.