A gravure printing unit (500) for printing onto substrate (S) according to a gravure printing method, said gravure printing unit having a forme cylinder (503), which comprises on its circumference an image-forming pattern of recesses (514), and having an inking unit (508) for inking the pattern of recesses (514) provided on the forme cylinder (503), said inking unit comprising a first inking unit cylinder (512), which comprises recesses (513) in the region of its outer cylindrical surface (518) that correspond to recesses (514) on the forme cylinder (503), and which forms a nip point downstream with a second inking unit cylinder (519), which comprises on its circumference ink-transferring elevations (524;
- 524′) or raised areas (522), characterized in that the recesses (513) on the first inking unit cylinder (512) are provided on the outer circumference of a in the form of a circumferentially closed ink transfer forme sheath (637), and in that the first inking unit cylinder (512) is configured as temperature controllable.