In the 'recent' geologic past, sea levels have fluctuated from 10 meters higher than they are today, to 200 meters lower than they are today. we are in an interglacial period. the polar ice caps are already mostly melted. There will be no 'dramatic' rise in sea levels. Just move a couple of yards up the beach, and you are set.
Oh, and the temperature in 0 AD was cooler than it is today. It was later, 400 AD to 1300 AD that it was warmer. But, the last time that all the polar ice was melted is now called the Mid Eocene Climactic Optimum. The name comes from the fact that there were more species in greater numbers than any time since.
Predictions of famine are premature at best.