The Rosette molecular cloud has a characteristic morphology, where the central OB cluster NGC 2244 has blown a circular-shaped cavity into the cloud and the expanding HII-region now interacts with the cloud. We use continuum data obtained with the PACS (70 and 160 μm) and SPIRE instruments (250, 350, 500 μm) of the Herschel telescope to investigate the spatial distribution of cold and warm gas and to locate all star-forming sites in Rosette. We detected a clear negative temperature gradient and a positive density gradient (running from the HII-region/molecular cloud interface into the cloud), and an age-sequence (from more evolved to younger) with increasing distance to the cluster NGC 2244. The existence of such temperature and density gradients and the observed age-sequence imply that star formation in Rosette may indeed be influenced by the radiative impact of the central NGC 2244 cluster.