03 Toyoto Corolla sputter/temp gauge problem?

Well if you flushed the cooling system twice and fixed the problem twice, sounds like you have a blockage in the cooling system somewhere. I would check to see if the thermostat is working correctly first. then go from there. About the sputtering, you may have a blown head gasket, and or a cracked head. Are you loosing coolant, or is the car smoking white? Just things to look for and look at.