Disentangling the effects of neutral and adaptive processes in maintaining phenotypic variation across environmental gradients is challenging in natural populations. Song sparrows (Melospiza melodia) on the California Channel Islands occupy a pronounced east-west climate gradient within a small spatial scale, providing a unique opportunity to examine the interaction of genetic isolation (reduced gene flow) and the environment (selection) in driving variation. We used reduced representation genomic libraries to infer the role of neutral processes (drift and restricted gene flow) and divergent selection in driving variation in thermoregulatory traits with an emphasis on the mechanisms that maintain bill divergence among islands. Analyses of 22,029 neutral SNPs confirm distinct population structure by island with restricted gene flow and relatively large effective population sizes, suggesting bill differences are probably not a product of genetic drift. Instead, we found strong support for local adaptation using 3294 SNPs in differentiation-based and environmental association analyses coupled with genome-wide association tests. Specifically, we identified several putatively adaptive and candidate loci in or near genes involved in bill development pathways (e.g., BMP, CaM, Wnt), confirming the highly complex and polygenic architecture underlying bill morphology. Furthermore, we found divergence in genes associated with other thermoregulatory traits (i.e., feather structure, plumage colour, and physiology). Collectively, these results suggest strong divergent selection across an island archipelago results in genomic changes in a suite of traits associated with climate adaptation over small spatial scales. Future research should move beyond studying univariate traits to better understand multidimensional responses to complex environmental conditions.