Potato is adapted to cool environments, and there is concern that its performance may be diminished considerably due to global warming and more frequent episodes of heat stress. Our objectives were to determine the response of potato plants to elevated CO2 (700 μmol/mol) and high temperature (35/25 °C) at tuber initiation and tuber bulking, and to elucidate effects on sink developmental processes. Potato plants were grown in controlled environments with treatments at: Tuber initiation (TI), during the first two weeks after initiating short-day photoperiods, and Tuber bulking (TB). At TI, and 25 °C, elevated CO2 increased tuber growth rate, while leaves and stems were not affected. Whole-plant dry matter accumulation rate, was inhibited by high temperature about twice as much at TI than at TB. Elevated CO2 partially ameliorated high temperature inhibition of sink organs. At TI, with 25 °C, elevated CO2 primarily affected tuber cell proliferation. In contrast, tuber cell volume and endoreduplication were unaffected. These findings indicate that the TI stage and cell division is particularly responsive to elevated CO2 and high temperature stress, supporting the view that attention should be paid to the timing of high-temperature stress episodes with respect to this stage.