Apparatus for tempering a substrate, in particular a wafer substrate, having: a plate-shaped main body (1; 1a, 1b) having a substrate bearing surface; a first tempering device for tempering the main body by means of a first tempering fluid and said first tempering device comprises a first plurality of separate annular ducts (R1F-R4F) in the interior of the main body (1; 1a, 1b) for circulating the first tempering fluid; a second tempering device for tempering the main body by means of a second tempering fluid and said second tempering device comprises a second plurality of separate annular ducts (R1L-R5L) in the interior of the main body (1; 1a, 1b) for circulating the second tempering fluid; wherein the first plurality of separate annular ducts (R1F-R4F) and the second plurality of separate annular ducts (R1L-R5L) are arranged alternately encompassing one another; wherein it is possible to supply the first tempering fluid to the first plurality of annular ducts (R1F-R4F) through a first tube (K1F) and it is possible through a second tube (K2F) to drain said first tempering fluid from said first plurality of annular ducts, wherein it is possible to supply the second tempering fluid to the second plurality of annular ducts (R1L-R5L) through a third tube (K1L) and it is possible through a fourth tube (K2L) to drain said second tempering fluid from said second plurality of annular ducts; wherein the main body (1; 1a, 1b) comprises a first to fourth hole (B1F, B2F, B1L, B2L) and said holes in each case communicate with the first plurality of separate annular ducts (R1F-R4F) and the second plurality of separate annular ducts (R1L-R5L); wherein the first tube (K1F) is inserted into the first hole (B1F) of the main body (1: 1a, 1b) and comprises respective first openings (F1-F4) in the region of the first plurality of separate annular ducts (R1F-R4F) for supplying the first tempering fluid; wherein the second tube (K2F) is inserted into the second hole (B2F) of the main body (1: 1a, 1b) and comprises respective second openings (F1'-F4') in the region of the first plurality of separate annular ducts (R1F-R4F) for draining the first tempering fluid; wherein the third tube (K1L) is inserted into the third hole (B1L) of the main body (1: 1a, 1b) comprises respective third openings (L1-L4) in the region of the second plurality of separate annular ducts (R1L-R5L) for supplying the second tempering fluid; wherein the fourth tube (K2L) is inserted into the fourth hole (B2L) of the main body (1: 1a, 1b) and comprises respective fourth openings (L1'-L5') in the region of the second plurality of separate annular ducts (R1L-R5L) for draining the second tempering fluid. a plate-shaped main body (1; 1a, 1b) having a substrate bearing surface; a first tempering device for tempering the main body by means of a first tempering fluid and said first tempering device comprises a first plurality of separate annular ducts (R1F-R4F) in the interior of the main body (1; 1a, 1b) for circulating the first tempering fluid; a second tempering device for tempering the main body by means of a second tempering fluid and said second tempering device comprises a second plurality of separate annular ducts (R1L-R5L) in the interior of the main body (1; 1a, 1b) for circulating the second tempering fluid; wherein the first plurality of separate annular ducts (R1F-R4F) and the second plurality of separate annular ducts (R1L-R5L) are arranged alternately encompassing one another; wherein it is possible to supply the first tempering fluid to the first plurality of annular ducts (R1F-R4F) through a first tube (K1F) and it is possible through a second tube (K2F) to drain said first tempering fluid from said first plurality of annular ducts, wherein it is possible to supply the second tempering fluid to the second plurality of annular ducts (R1L-R5L) through a third tube (K1L) and it is possible through a fourth tube (K2L) to drain said second tempering fluid from said second plurality of annular ducts; wherein the main body (1; 1a, 1b) comprises a first to fourth hole (B1F, B2F, B1L, B2L) and said holes in each case communicate with the first plurality of separate annular ducts (R1F-R4F) and the second plurality of separate annular ducts (R1L-R5L); wherein the first tube (K1F) is inserted into the first hole (B1F) of the main body (1: 1a, 1b) and comprises respective first openings (F1-F4) in the region of the first plurality of separate annular ducts (R1F-R4F) for supplying the first tempering fluid; wherein the second tube (K2F) is inserted into the second hole (B2F) of the main body (1: 1a, 1b) and comprises respective second openings (F1'-F4') in the region of the first plurality of separate annular ducts (R1F-R4F) for draining the first tempering fluid; wherein the third tube (K1L) is inserted into the third hole (B1L) of the main body (1: 1a, 1b) comprises respective third openings (L1-L4) in the region of the second plurality of separate annular ducts (R1L-R5L) for supplying the second tempering fluid; wherein the fourth tube (K2L) is inserted into the fourth hole (B2L) of the main body (1: 1a, 1b) and comprises respective fourth openings (L1'-L5') in the region of the second plurality of separate annular ducts (R1L-R5L) for draining the second tempering fluid.