A method for producing a polymer from a first component and a second component using a reactor (50) offers technical advantages, wherein reaction heat produced in the reactor (50) is discharged via a boiling cooler (40) by supplying gaseous vapors produced in the reactor (50) to the boiling cooler (40). A product flow containing condensed vapors is returned to the reactor (50) from the boiling cooler (40) via a separation vessel (60), and an aqueous phase is separated from the product flow in the separation vessel (60). A system is provided for producing a polymer from a first component and a second component, comprising a reactor (50) and a boiling cooler (40) for discharging reaction heat produced in the reactor (50). A separation vessel (60) is arranged between the boiling cooler (40) and the reactor (50) such that a product flow containing condensed vapors is returned to the reactor (50) from the boiling cooler (40) via the separation vessel (60).