Fluctuating environments are expected to select for individuals that have highest geometric fitness over the experienced environments. This leads to the prediction that genetically determined environmental robustness in fitness, and average fitness across environments should be positively genetically correlated to fitness in fluctuating environments. Because quantitative genetic experiments resolving these predictions are missing, we used a full-sib, half-sib breeding design to estimate genetic variance for egg-to-adult viability in Drosophila melanogaster exposed to two constant or fluctuating temperatures that were above the species' optimum temperature, during development. Viability in two constant environments (25°C or 30°C) was used to estimate breeding values for environmental robustness of viability (i.e., reaction norm slope) and overall viability (reaction norm elevation). These breeding values were regressed against breeding values of viability at two different fluctuating temperatures (with a mean of 25°C or 30°C). Our results based on genetic correlations show that average egg-to-adult viability across different constant thermal environments, and not the environmental robustness, was the most important factor for explaining the fitness in fluctuating thermal environments. Our results suggest that the role of environmental robustness in adapting to fluctuating environments might be smaller than anticipated.