Generative adversarial networks (GANs) are one of the most robust and versatile techniques in the field of generative artificial intelligence. In this work, we report on an application of GANs in the domain of synthetic spectral data generation, offering a solution to the scarcity of data found in various scientific contexts. We demonstrate the proposed approach by applying it to an illustrative problem within the realm of near-field radiative heat transfer involving a multilayered hyperbolic metamaterial. We find that a successful generation of spectral data requires two modifications to conventional GANs: (i) the introduction of Wasserstein GANs (WGANs) to avoid mode collapse, and, (ii) the conditioning of WGANs to obtain accurate labels for the generated data. We show that a simple feed-forward neural network (FFNN), when augmented with data generated by a CWGAN, enhances significantly its performance under conditions of limited data availability, demonstrating the intrinsic value of CWGAN data augmentation beyond simply providing larger datasets. In addition, we show that CWGANs can act as a surrogate model with improved performance in the low-data regime with respect to simple FFNNs. Overall, this work highlights the potential of generative machine learning algorithms in scientific applications beyond image generation and optimization.