Parental history of opioid exposure is seldom considered when prescribing opioids for pain relief. To explore whether parental opioid exposure may affect sensitivity to morphine in offspring, we developed a “rat pain scale” with high-speed imaging, machine learning, and mathematical modeling in a multigenerational model of paternal morphine self-administration. We find that the most commonly used tool to measure mechanical sensitivity in rodents, the von Frey hair, is not painful in rats during baseline conditions. We also find that male progeny of morphine-treated sires had no baseline changes in mechanical pain sensitivity but were more sensitive to the pain-relieving effects of morphine. Using RNA sequencing across pain-relevant brain regions, we identify gene expression changes within the regulator of G protein signaling family of proteins that may underlie this multigenerational phenotype. Together, this rat pain scale revealed that paternal opioid exposure increases sensitivity to morphine’s pain-relieving effects in male offspring.