1997 Mitsubishi Eclipse car purges coolant

2 months ago, I was driving 30 mph and my thermostat started going up. I turned off the engine, looked behind me and saw a trail of coolant going down the street. After adding water and antifreeze, the car was fine. No leaks or anything. Last night, the same thing happened. I was driving around 70 mph and saw my thermostat going up. When I looked under the car, I saw coolant dripping underneath my engine. Once again, I added water and coolant and drove the car home. It looks fine now (no leaks or anything). Why is my car purging its coolant? Do I have to replace the thermostat?