Drain and rinse sauerkraut; set aside.
In a 4-qt. pot, heat oil over medium-high heat. Add onions and cook, stirring occasionally, until softened, about 3 minutes. Add caraway seeds and cook, stirring, until combined, about 1 minute. Stir in sauerkraut and ale. Reduce heat to medium-low and cook, stirring once in a while, until the mixture is hot and flavors are blended, about 30 minutes. Serve warm or at room temperature.
Note: Nutritional analysis is per serving.