To gain panoramic awareness of spectrum coverage in complex wireless environments, data-driven learning approaches have recently been introduced for radio map estimation (RME). While existing deep learning based methods conduct RME given spectrum measurements gathered from dispersed sensors in the region of interest, they rely on centralized data at a fusion center, which however raises critical concerns on data privacy leakages and high communication overloads. Federated learning (FL) enhance data security and communication efficiency in RME by allowing multiple clients to collaborate in model training without directly sharing local data. However, the performance of the FL-based RME can be hindered by the problem of task heterogeneity across clients due to their unavailable or inaccurate landscaping information. To fill this gap, in this paper, we propose a physics-inspired distributed RME solution in the absence of landscaping information. The main idea is to develop a novel distributed RME framework empowered by leveraging the domain knowledge of radio propagation models, and by designing a new distributed learning approach that splits the entire RME model into two modules. A global autoencoder module is shared among clients to capture the common pathloss influence on radio propagation pattern, while a client-specific autoencoder module focuses on learning the individual features produced by local shadowing effects from the unique building distributions in local environment. Simulation results show that our proposed method outperforms the benchmarks in achieving higher performance.