Leaking coolant underneath

When I drive my car for awhile and put it in park the engine idles is high. When I turn it off, I notice my coolant running out. But it never overheats. When the engine cool I check the reservoir and the coolant is low. I start the engine and the idle is still high. I top it off with coolant and the idle drips down to normal. But the car never runs hot. What could cause that?