We propose a diagnostic tool, a temperature estimator, for lattice gauge theory simulations. The estimator is obtained from the gradient and the Hessian of the Euclidean lattice action. It is gauge invariant, configuration-based, and independent of momentum-space information. These features enable direct checks of thermodynamic consistency in Monte Carlo simulations. We apply this tool to compact U(1) lattice gauge theories in one, two, and four dimensions. The results confirm the proposed estimator's ability to reproduce the input temperatures across different lattice ensembles. The estimator is sensitive to sampling inefficiencies and algorithmic artifacts, making it a useful diagnostic for large-scale simulations.