Viral cross-species transmission is recognized to be a major threat to both human and animal health, however detailed information on determinants underlying virus host tropism and susceptibility is missing. Influenza C and D viruses (ICV, IDV) are two respiratory viruses that share up to 50% genetic similarity, and both employ 9-O-acetylated sialic acids to enter a host cell. While ICV infections are mainly restricted to humans, IDV possesses a much broader host tropism and has shown to have a zoonotic potential. This suggests that additional virus–host interactions play an important role in the distinct host spectrum of ICV and IDV. In this study, we aimed to characterize the innate immune response of the respiratory epithelium of biologically relevant host species during influenza virus infection to identify possible determinants involved in viral cross-species transmission. To this end, we performed a detailed characterization of ICV and IDV infection in primary airway epithelial cell (AEC) cultures from human, porcine, and bovine origin. We monitored virus replication kinetics, cellular and host tropism, as well as the host transcriptional response over time at distinct ambient temperatures. We observed that both ICV and IDV predominantly infect ciliated cells, independently from host and temperature. Interestingly, temperature had a profound influence on ICV replication in both porcine and bovine AEC cultures, while IDV replicated efficiently irrespective of temperature and host. Detailed time-resolved transcriptome analysis revealed both species-specific and species uniform host responses and highlighted 34 innate immune-related genes with clear virus-specific and temperature-dependent profiles. These data provide the first comprehensive insights into important common and species-specific virus-host dynamics underlying the distinct host tropism of ICV and IDV, as well as possible determinants involved in viral cross-species transmission.