Went a few hundred miles with engine heat sporadically going up and down from 230 to 245. Stopped at radiator shop to check thermostat and was very low on antifreeze. Topped it off but problem only got worse. Radiator guy says egr cooler wasn't working right. It was allowing antifreeze to be leaked thru exhaust. But even after topping off temp reached maximums so I towed home. No external antifreeze leaks. Can the egr cooler cause this overheating problem?