What makes a car sputter?
A malfunctioning battery can't provide enough power to your ignition system when the motor is idling can cause sputtering. If there is not enough gas, that can cause your vehicle to sputter. If the spark plugs fail to fire will also cause your vehicle to sputter.
Can a faulty thermostat on a 97 eclipse cause the car to run poorly after heating up spit and sputter?
The car will act like it is out of gas, sputter and eventually die, if there is enough water in the tank. If there is only a little bit, it will ususally sputter just a little before it evaporates the water. Still, no matter what happens with the water, you will need to replace the fuel filter, which is how the water got in there in the first place.