The domestication process has resulted in profound changes in the reproductive physiology of the animals that might have affected the sperm characteristics and thus their sensitivity to handling and cryopreservation procedures. This work assesses the response of the sperm of domestic and wild ungulates to a cooling storage at 15°C for 20 h followed by incubation at 38.5°C, 5% CO2, for 2 h. In addition, this paper examines the most representative sperm traits to assess their responsiveness to these stress conditions. Sperm samples were collected from domestic and their wild ancestor species: ram, mouflon, buck, Iberian ibex, domestic boar, and wild boar. Sperm motility, viability, mitochondrial membrane status, DNA fragmentation, and reactive oxygen species production were evaluated at the beginning of the experiment, after 20 h of refrigeration at 15°C, and, finally, at 2 h of incubation at 38.5°C. Sperm from all domestic species (ram, buck, and domestic boar) suffered more stress than their wild relatives (mouflon, Iberian Ibex, and wild boar). In pigs, the percentage of intact mitochondria was lower in the domestic species compared to wild boar. In sheep, we found a higher reactive oxygen species production in rams, while in goats, the curvilinear velocity was lower in the domestic species. The PCA (principal components analysis) showed that the motility and their kinetic variables were the most represented variables in the principal components of all species, indicating that they are essential biomarkers for evaluating the stress response. Sperm viability was highlighted as a representative variable for evaluating the stress response in domestic boar, mouflon, ram, and ibex.