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Understanding biodiversity changes in time is crucial to promptly provide management practices against diversity loss. This is overall true when considering global scales, since human-induced global change is expected to make significant changes on the Earth's biota. Biodiversity management and planning is mainly based on field observations related to community diversity, considering different taxa. However, such methods are time and cost demanding and do not allow in most cases to get temporal replicates. In this view, remote sensing can provide a wide data coverage in a short period of time. Recently, the use of Rao's Q diversity as a measure of spectral diversity has been proposed in order to explicitly take into account differences in a neighbourhood considering abundance and relative distance among pixels. The aim of this paper was to extend such a measure over the temporal dimension and to present an innovative approach to calculate remotely sensed temporal diversity. We demonstrated that temporal beta-diversity (spectral turnover) can be calculated pixel-wise in terms of both slope and coefficient of variation and further plotted over the whole matrix / image. From an ecological and operational point of view, for prioritisation practices in biodiversity protection, temporal variability could be beneficial in order to plan more efficient conservation practices starting from spectral diversity hotspots in space and time. In this paper, we delivered a highly reproducible approach to calculate spatio-temporal diversity in a robust and straightforward manner. Since it is based on open source code, we expect that our method will be further used by several researchers and landscape managers.