Physics-informed neural networks (PINNs) are known to suffer from spectral bias when applied to systems with high-frequency dynamics, a limitation that becomes particularly severe in high-dimensional problems with increased optimization complexity. In this work, we develop a physics-informed Kolmogorov–Arnold Network (PIKAN) trained using a quasi-second-order optimizer and probabilistic, adaptive resampling to solve an unsteady three-dimensional heat conduction problem with boiling boundary conditions. The boiling boundary condition incorporates realistic bubble dynamics extracted from experimental infrared measurements during pool boiling, enabling the estimation of the spatiotemporal boiling heat flux at the boundary. Our results demonstrate that PIKAN exhibits superior representational capacity for capturing high-frequency bubble dynamics compared to a PINN trained for the same computational time. This improved expressiveness leads to markedly better resolution of the tail of the heat-flux distribution, which is associated with bubble interface regions. We further show that the commonly used Adam optimizer fails to adequately optimize the network in this setting, resulting in the loss of bubble dynamics. In contrast, the quasi-second-order SOAP optimizer accurately captures high-frequency features and evolving bubble interfaces, underscoring the critical role of both optimization strategy and network architecture in mitigating spectral bias. In addition, we demonstrate that PIKAN is significantly more robust to experimental noise than conventional finite-difference methods. Even small levels of noise in boundary temperature measurements propagate through numerical solvers and produce large, unphysical oscillations in the inferred heat-flux field, whereas such noise is effectively filtered by the neural network, highlighting a key advantage of the proposed approach over traditional numerical techniques.