Accurate temperature monitoring in automated test equipment (ATE) is crucial for ensuring the reliability and quality of semiconductor testing. However, ATE temperature models often rely on noisy, sparsely-sampled sensor data, and existing methods struggle to update models efficiently as operating conditions evolve. This paper presents Neighbor-Pseudo-GP, a probabilistic online method for modeling the temperature distribution of an ATE board. Our approach uses a Gaussian process (GP) to represent the entire field from a small number of observations while explicitly accounting for time-varying noise. Unlike variational methods that rely on sparse inducing points and assume homogeneous noise, we recursively merge new observations with the full posterior of the latest model under heterogeneous noise, achieving O(1) time and memory complexity. In addition, we design a specialized spatio-temporal kernel that clearly separates spatial and temporal effects. Experiments on synthetic data demonstrate precise estimation of time-varying noise variance and effective noise filtering. Results on semiconductor burn-in data confirm that our model reliably reconstructs the underlying temperature field, closely matches ideal sensor measurements, and adapts robustly to non-stationary conditions.