The physical state of the Baltic Sea in possible future climates is approached by numerical model experiments with a regional coupled ocean-atmosphere model driven by different global simulations. Scenarios and recent climate simulations are compared to estimate changes. The sea surface is clearly warmer by 2.9 degrees C in the ensemble mean. The horizontal pattern of average annual mean warming can largely be explained in terms of ice-cover reduction. The transfer of heat from the atmosphere to the Baltic Sea shows a changed seasonal cycle: a reduced heat loss in fall, increased heat uptake in spring, and reduced heat uptake in summer. The interannual variability of surface temperature is generally increased. This is associated with a smoothed frequency distribution in northern basins. The overall heat budget shows increased solar radiation to the sea surface, which is balanced by changes of the other heat flux components.