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The genetic architecture of adaptive traits is of key importance to predict evolutionary responses. Most adaptive traits are polygenic–ie result from selection on a large number of genetic loci–but most molecularly characterized traits have a simple genetic basis. This discrepancy is best explained by the difficulty in detecting small allele frequency changes across many contributing loci. To resolve this, we use laboratory natural selection, a framework that is powerful enough to detect signatures for selective sweeps and polygenic adaptation. We exposed 10 replicates of a Drosophila simulans population to a new temperature regime and uncovered a polygenic architecture of an adaptive trait with high genetic redundancy among adaptive alleles. We observed convergent phenotypic responses, eg fitness, metabolic rate and fat content, and a strong polygenic response (99 selected alleles; mean s= 0.061). However, each of these selected alleles increased in frequency only in a subset of the evolving replicates. Our results show that natural D. simulans populations harbor a vast reservoir of adaptive variation facilitating rapid evolutionary responses. The observed genetic redundancy potentiates this genotypic variation through multiple genetic pathways leading to phenotypic convergence. This key property of adaptive alleles requires the modification of testing strategies in natural populations beyond the search for convergence on the molecular level.