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Urban heat exposure assessment requires continuous, physically interpretable thermal fields, yet satellite-derived land surface temperature (LST)—the most widely used spatial heat indicator—remains fragmented by clouds and complex surface heterogeneity. We introduce SEB-TwinTFT, a physics-guided hybrid modelling framework that reconstructs daily gap-free urban LST with quantified uncertainty while jointly inferring effective surface energy balance (SEB) parameters. Unlike conventional deep networks that only emulate LST, SEB-TwinTFT produces time-evolving maps of effective albedo (α), aerodynamic resistance (ra), evaporative efficiency (β), and ground heat flux fraction (γ). Constraining the network to explain LST through these quantities turns SEB into a structural prior, reduces black-box behaviour, and provides a mechanistic view of urban heat island amplification, diurnal coupling and decoupling, and lake–land interactions. Architecturally, SEB-TwinTFT couples a temporal-fusion transformer head with a differentiable SEB head through a learnable gate that adaptively blends data-driven and physics-based predictions. Applied to summers in Geneva over 2000–2024, the framework reproduces spatial and temporal LST variability, recovers diurnally consistent SEB fields, and reveals a systematic lakeward displacement of nocturnal hotspots consistent with land-breeze advection not explicitly encoded in the SEB equations. Cross-decadal validation with a strict 2011–2020 hold-out demonstrates robust skill for both typical conditions and upper-tail LST extremes. Clear-sky sampling bias in thermal infrared data is mitigated via inverse-probability weighting of Missing-Not-at-Random observations, and a heteroscedastic likelihood yields well-calibrated prediction intervals. SEB-TwinTFT advances physics-guided machine learning for urban climate by delivering mechanism-aware, uncertainty-quantified products for diagnosing, attributing, and managing urban heat exposure in complex lake–urban environments.