This paper systematically derives and analyses the generic phenomenon of space-invariant predictability of spatio-temporal observation fields using past multitemporal observations. We focus on thermal infrared remote sensing as a non-trivial example illustrating the predictability concept. The phenomenon and the systematic analysis thereof are experimentally demonstrated to be productive for developing effective automated anomaly detection and classification methods operating under the assumption of dynamic environment and sensor response. Using a simple preliminary experiment involving uncalibrated tower-based high-resolution thermal infrared surveillance, we test the conceptual validity of the space-invariant multitemporal prediction and exemplify its potential applications. In addition, we use a MODIS thermal image sequence and the task of hot anomaly detection to demonstrate the applicability of the approach for monitoring the status of large territories from space-borne platforms.