We develop a semiparametric kinematic state-space framework for estimating the latent dynamics of global warming from noisy monthly temperature observations. The framework estimates the warming level, warming rate, and warming acceleration jointly, while incorporating covariates, measurement error, serial dependence, and time-varying error variance directly in the model. Applying the framework to five major global temperature records, and comparing it with nonparametric kernel and parametric benchmark estimators, we show that the inferred recent warming dynamics depend crucially on the parametric restrictions imposed on the warming path. The current underlying warming level is robustly estimated across datasets and methods, with estimates close to \(1.40\,^{\circ}\mathrm{C}\) above pre-industrial levels. Estimates of the current warming rate differ materially across estimator classes: flexible local estimators imply substantially higher current rates than the parametric benchmarks. Our preferred state-space specification estimates the current warming rate at approximately \(0.47\,^{\circ}\mathrm{C} \, \textnormal{decade}^{-1}\). Endpoint acceleration estimates from the flexible estimators are positive across all five records, although their statistical significance varies across records and methods. Average acceleration since 2015 is significantly positive across all five records in the preferred state-space model, with a cross-dataset mean of approximately \(0.19\,^{\circ}\mathrm{C} \, \textnormal{decade}^{-2}\). Our results indicate that global warming is proceeding faster, and has accelerated more strongly in the recent period, than conventional estimates suggest.

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