Circadian systems share the three properties of entrainment, free-running period, and temperature compensation (TC). TC ensures nearly the same period over a broad range of physiologically relevant temperatures; however, the mechanisms behind TC remain poorly understood. Here, we identify single point mutations in two key elements of the Arabidopsis circadian clock, GIGANTEA (GI) and ZEITLUPE (ZTL), which likely act as compensatory substitutions to establish a remarkably constant free-running period over a wide range of temperatures. Using near-isogenic lines generated from the introgression of the Cape Verde Islands (Cvi) alleles of GI and ZTL into the Landsberg erecta (Ler) background, we show how longer periods in the Cvi background at higher temperatures correlate with a difference in strength of the GI/ZTL interaction. Pairwise interaction testing of all GI/ZTL allelic combinations shows similar affinities for isogenic alleles at 22°C, but very poor interaction between GI (Cvi) and ZTL (Cvi) at higher temperature. In vivo, this would result in lower ZTL levels at high temperatures leading to longer periods in the Cvi background. Mismatched allelic combinations result in extremely strong or weak GI/ZTL interactions, indicating how the corresponding natural variants likely became fixed through epistatic selection. Additionally, molecular characterization of GI (Cvi) reveals a novel functional motif that can modulate the GI/ZTL interaction as well as nucleocytoplasmic partitioning. Taken together, these results identify a plausible temperature-dependent molecular mechanism, which contributes to the robustness of TC through natural variation in GI and ZTL alleles found on the Cape Verde Islands.