Q: Coolant keeps leaking

I have fond some iron sludge in my coolant before, but the car was fine after I flushed it. Last week, I got a "low coolant" light, and when I checked the level, it was completely dry, with nothing in the overflow either.

I added some, but about 50 miles later, it's low again. I checked the dipstick to make sure the oil is not over-full (no leaks into the oil - check). There is no antifreeze pooling under the car when it's parked, or under the hood. There's also no white smoke coming out the exhaust. The car seems to run fine, and there's not even a change in temperature. The only slightly odd thing is that it starts fine when the weather is cold, but takes longer to start when it's warm out. It's been like that for over a year though. Any pointers on what might be causing this?