How quickly you reach warmer weather depends on...the weather. Next week is supposed to be warmer in the south, which usually means the same for the Atlantic but you never can really tell for sure.
You need to pack like you are going to Alaska, which means layering. Bring a couple sweaters and perhaps a windbreaker type of jacket. That way you can adjust your attire as conditions change during the days at sea.
Most ships are cool inside, even in the dead of summer in the Caribbean. So once again those sweaters might be useful. I'd also consider some long-sleeved shirts or tops.