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Thermal error modeling (TEM) stands as a pivotal factor in maintaining the machining accuracy of electric spindles. Deep learning (DL) techniques have shown promising potential in this area, however, they face formidable challenges including domain shift issue between training and testing datasets, as well as scarce samples due to the dynamic nature of variable working conditions. Deep transfer learning (DTL) emerges as an encouraging tool, leveraging knowledge obtained from the source domain to elevate learning outcomes within the target domain, notably addressing complicated cross-domain modeling predicaments. Nonetheless, prevailing research largely focuses on enhancing the prediction accuracy within the specific working condition, inadvertently sidestepping the problems of domain shift and scarce sample modeling. To address these issues, a novel weakly supervised adversarial network (WSAN) is proposed for cross-domain TEM with scarce samples. Firstly, the multi-scale convolutional neural network (MSCNN) is constructed to adeptly extract predictive information from multi-sensor data, effectively capturing the time-series patterns embedded within. Furthermore, the adversarial training technique is adopted to address distribution discrepancies that often manifest between distinct domains. To overcome the challenge of scarce labeled samples in the target domain, a weakly supervised learning strategy is employed to deftly control the gradient within the target domain, significantly enhancing the efficacy of positive transfer. The effectiveness and superiority of the proposed method are assessed through extensive experiments using datasets from variable working conditions. The experimental results demonstrate that the proposed method achieves satisfactory performance and outperforms state-of-the-art approaches. [ABSTRACT FROM AUTHOR]