Recognising the increasing complexities posed by climate challenges to urban environments, it is crucial to develop holistic capabilities for urban areas to effectively respond to climate-related risks, forming the backbone of sustainable urban planning strategies and demanding a comprehensive understanding of urban climate justice. It requires a thorough examination of how climate change exacerbates social, economic, and environmental inequalities within urban settings, which requires a series of sophisticated spatial modellings and relies on data collected periodically. This paper introduces a novel dual-GNN approach, Multi-Hyper Graph Neural Network (MHGNN), with street view imagery as input. The proposed model integrates a multigraph and a hypergraph to model intricate spatial patterns for classifying urban climate justice. The multigraph component of the MHGNN captures spatial proximity and pair-wise connections between urban areas to assess climate impacts. Meanwhile, the hypergraph component addresses higher-order dependencies by incorporating hyperedges that connect multiple geographic areas based on their similarities, thus capturing the multi-faceted relationships among areas with comparable geographic characteristics. By harnessing the strengths of both multigraph and hypergraph structures, the MHGNN provides a comprehensive understanding of the spatial dynamics of urban climate justice. It achieves nearly a 24% performance improvement compared to conventional spatial modelling methods, establishing it as a valuable tool for researchers and policymakers in this domain. Codes available at GitHub.