How is achieved the loss of heat through vasodilation? I know it is the widening of blood vessels, loosing heat in this way. But is it achieved through: sweat evaporation, the increase of cardiac rhythm, the increase of respiratory/ breathing rhythm or frequent urination?

Sweat evaporation is the most correct answer you have mentioned. Vasodilation increases blood flow, allowing for more blood to be cooled be vessels closer to the surface of the skin. It's increasing the surface area the blood interacts with, which always allows for faster heat transfer.