This phase I trial studies the side effects and best dose of aldesleukin when given together with pembrolizumab in treating patients with kidney cancer that has spread to other parts of the body. Aldesleukin may stimulate white blood cells to kill kidney cancer cells. Monoclonal antibodies, such as pembrolizumab, may interfere with the ability of tumor cells to grow and spread. Giving aldesleukin and pembrolizumab may work better in treating patients with kidney cancer.