Yes, the warmer water allowed the dough to start to ferment and that meant that it would take longer for the refrigerator to cool the dough down.
During the time that the dough is in the refrigerator, the enzymes and bacteria can still perform, even if slowed down a bit, resulting in increased byproducts of fermentation that contribute to the flavor, color, aroma and texture of the finished crust. Some people, including many professionals, like to work with cold fermented doughs rather than room temperature fermented doughs because it is easier to work with and manage cold fermented doughs than room temperature fermented doughs that can be subject to many variations in room temperature, including seasonal variations over the course of a year. Cold fermentation is also more conducive to inventory control because dough balls can be held in storage longer and not thrown away or recycled, as might occur with room-temperature dough balls that are not used by the end of the day. For most of us who are not professionals, the main reason for using cold fermented dough is because of the positive attributes mentioned above.