I have water/coolant in my transmission fluid. How could it have gotten there?

I noticed low coolant three months ago. I wondered where the water went, but experienced no car problems, so I refilled it. It got a bit low again and I did the same thing. Yesterday, the "w' light came on and the car was not shifting properly. I checked the transmission fluid level and it looked like a vanilla milkshake. I drained the transmission fluid, refilled it, drove it a few blocks. It shifted pretty well. I checked the level again and the color of the fluid looked better, like strawberry milk this time. The transmission fluid level remained the same, indicating no new water/coolant got in. After it sat overnight I drove it. While the transmission was cool it shifted poorly. As it warmed up it shifted better.