In the context of climate change, livestock production systems face the challenge of ensuring that, although more and more exposed to heat-stress conditions, animals will be able to remain healthy while maintaining satisfactory production, responding to consumer's demand. As part of the European project RUMIGEN, France (INRAE, Idele), Spain (INIA, IRIAF), and the Netherlands (WUR) studied the response of different dairy traits to heat-stress conditions for Holstein cattle breed. Production (milk, fat and protein yields) and udder health (somatic cell score) traits were investigated under different meteorological conditions, represented by the temperature humidity index (THI) averaged over three days on the day of recording and the two days before. A THI=50 was considered as neutral condition (i.e. no heat/cold-stress) and used as reference for level comparisons. Specific rates of changes in production/health traits at a given THI were measured as the slopes (first derivative) of the estimated reaction-norm curves for each trait. Genetic evaluations were performed by each country using test-day records of cows in their first lactation between 2010 and 2020, to estimate both levels and slopes for each trait. Estimated breeding values (EBVs) and reliabilities were obtained for sires with at least 20 daughters with test-day records. A meta-analysis was performed to estimate the genetic correlations between the three countries, using the Multiple Across Country Evaluation approach. For each country, de-regressed proofs (DRPs) and effective record contributions (ERCs) were computed using a single trait model from the EBVs, reliabilities, and variance components estimated at a national level for specific THI values. The estimated genetic correlations obtained with slopes were weak and not credible, which could be explained by the low heritability of the slopes and by the small proportion of performances recorded under heatstress conditions. The DRPs on slopes, as they were calculated, were not able to capture the genetic (co)variability associated to these traits. Conversely, estimated genetic correlations for all level traits were high (between 0.81 and 0.97) even if they were slightly lower than under thermo-neutral conditions. This shows a very good consistency of the three national genetic evaluations under heat-stress conditions. In conclusion, valuable predictions under heat-stress conditions could be obtained through international evaluations, that would result in Northern countries benefiting from the information that already exists in the Southern countries. However, the approach for low heritable traits such as slopes should be improved if there are not enough data at high THI.