Learning neural solvers for spatiotemporal partial differential equations (PDEs) under real-world constraints remains a key challenge in scientific machine learning, especially for inverse tasks with sparse and noisy boundary observations. We present the Aletheia dataset, the first 3D benchmark for learning data-driven solvers in the context of nondestructive testing (NDT). The dataset simulates eddy-current-induced heating in conductive solids and models the resulting transient heat propagation governed by the heat equation. Aletheia contains over 4,700 high-resolution samples across 10 excitation frequencies (1-100,kHz), each providing volumetric heat source and temperature fields over time. It supports both forward prediction of temperature evolution and inverse reconstruction of internal heat sources or defects from surface infrared measurements. Real infrared thermography data from cracked rail specimens are included for calibration and comparison. We define four canonical tasks on both regular and irregular grids and benchmark them using various neural operators. Aletheia establishes a unified platform for evaluating neural PDE solvers under realistic NDT conditions, enabling progress in reliable, data-driven inverse modeling. The dataset and code are publicly available at https://github.com/sherlock-0327/ALETHEIA.

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