Heat exchanger for an oxygenator, comprising a. a base body, b. a heat exchanger body arranged in the base body, said heat exchanger body comprising a mat with several plastic tube portions each having a longitudinal axis, said plastic tube portions i. being interconnected by means of retaining members running transversely to the longitudinal axis, ii. having an inlet opening allowing a heat exchanger medium to enter, iii. having a discharge opening allowing the heat exchanger medium to be discharged, and iv. containing polyurethane, c. wherein the heat exchanger body has blood flow passages adjacent to the plastic tube portions, each of said blood flow passages comprising a blood inlet opening and a blood discharge opening, d. wherein a direction of heat exchanger medium flow is defined by the arrangement of the inlet openings and discharge openings at the heat exchanger, e. wherein a direction of blood flow is defined by the arrangement of the blood inlet openings at one end of the blood flow passages and blood discharge openings at an end of the blood flow passages opposite to said one end, characterised in that f. the base body has a tubular shape and has a central longitudinal axis, g. the mat of the heat exchanger body is rolled up into a roll, h. the longitudinal axes of the plastic tube portions are oriented parallel to the central longitudinal axis, i. the direction of heat exchanger medium flow is oriented opposite to the direction of blood flow, j. the direction of blood flow is oriented along the central longitudinal axis of the base body. a. a base body, b. a heat exchanger body arranged in the base body, said heat exchanger body comprising a mat with several plastic tube portions each having a longitudinal axis, said plastic tube portions i. being interconnected by means of retaining members running transversely to the longitudinal axis, ii. having an inlet opening allowing a heat exchanger medium to enter, iii. having a discharge opening allowing the heat exchanger medium to be discharged, and iv. containing polyurethane, i. being interconnected by means of retaining members running transversely to the longitudinal axis, ii. having an inlet opening allowing a heat exchanger medium to enter, iii. having a discharge opening allowing the heat exchanger medium to be discharged, and iv. containing polyurethane, c. wherein the heat exchanger body has blood flow passages adjacent to the plastic tube portions, each of said blood flow passages comprising a blood inlet opening and a blood discharge opening, d. wherein a direction of heat exchanger medium flow is defined by the arrangement of the inlet openings and discharge openings at the heat exchanger, e. wherein a direction of blood flow is defined by the arrangement of the blood inlet openings at one end of the blood flow passages and blood discharge openings at an end of the blood flow passages opposite to said one end, f. the base body has a tubular shape and has a central longitudinal axis, g. the mat of the heat exchanger body is rolled up into a roll, h. the longitudinal axes of the plastic tube portions are oriented parallel to the central longitudinal axis, i. the direction of heat exchanger medium flow is oriented opposite to the direction of blood flow, j. the direction of blood flow is oriented along the central longitudinal axis of the base body.