The impact of climate change on populations will be contingent upon their contemporary adaptive evolution. In this study, we investigated the contemporary evolution of four populations of the cold-water kelp Laminaria digitata by analysing their spatial and temporal genomic variation using ddRAD-sequencing. These populations were sampled from the center to the southern margin of its north-eastern Atlantic distribution at two-time points, spanning at least two generations. Through genome scans for local adaptation at a single time point, we identified candidate loci that showed clinal variation correlated with changes in sea surface temperature (SST) along latitudinal gradients. This finding suggests that SST may drive the adaptive response of these kelp populations, although factors such as species' demographic history should also be considered. Additionally, we performed a simulation approach to distinguish the effect of selection from genetic drift in allele frequency changes over time. This enabled the detection of loci in the southernmost population that exhibited temporal differentiation beyond what would be expected from genetic drift alone: these are candidate loci which could have evolved under selection over time. In contrast, we did not detect any outlier locus based on temporal differentiation in the population from the North Sea, which also displayed low and decreasing levels of genetic diversity. The diverse evolutionary scenarios observed among populations can be attributed to variations in the prevalence of selection relative to genetic drift across different environments. Therefore, our study highlights the potential of temporal genomics to offer valuable insights into the contemporary evolution of marine foundation species facing climate change.