Accurate contact temperature estimation is critical for protection triggering and safe operation in uninterruptible power meter replacement devices, yet the contact interface is embedded inside the breaker and cannot be measured directly. In practice, only a few temperatures from accessible adjacent components can be obtained, which makes the transient boundary inverse heat conduction problem severely ill-posed and unstable under sparse measurements. To address this issue, we propose a transient temperature compensation framework based on a Compressive Sensing–Whale Optimization Algorithm (CSWOA). A second-order transient heat conduction forward model is constructed using the Dual Reciprocity Boundary Element Method (DRM–BEM), and the unknown boundary temperature is represented in a sparse coefficient domain to reduce the optimization dimensionality. Meanwhile, the sparse-recovery mechanism in compressive sensing is integrated into an improved whale optimization strategy to enhance inversion stability and convergence when observations are limited. Electro–thermal coupled simulations in ANSYS Workbench under two representative steady-state currents (40A and 10A) demonstrate that the proposed CSWOA reconstructs the bottom-boundary temperature with a mean absolute error below 1 ℃ and yields temperature distributions closely matching the simulation reference field. Compared with Particle Swarm Optimization (PSO) and the standard whale optimization algorithm, CSWOA achieves markedly improved accuracy and robustness, indicating its feasibility for contact temperature compensation in uninterruptible meter replacement connectors.