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The global statistical median behavior of the electron temperature (<i>T</i>_e) in the topside ionosphere was investigated through in-situ data collected by Langmuir Probes on-board the European Space Agency Swarm satellites constellation from the beginning of 2014 to the end of 2020. This is the first time that such an analysis, based on such a large time window, has been carried out globally, encompassing more than half a solar cycle, from the activity peak of 2014 to the minimum of 2020. The results show that Swarm data can help in understanding the main features of <i>T</i>_e in the topside ionosphere in a way never achieved before. <i>T</i>_e data measured by Swarm satellites were also compared to data modeled by the empirical climatological International Reference Ionosphere (IRI) model and data measured by Jicamarca (12.0°S, 76.8°W), Arecibo (18.2°N, 66.4°W), and Millstone Hill (42.6°N, 71.5°W) Incoherent Scatter Radars (ISRs). Moreover, the correction of Swarm <i>T</i>_e data recently proposed by Lomidze was applied and evaluated. These analyses were performed for two main reasons: (1) to understand how the IRI model deviates from the measurements; and (2) to test the reliability of the Swarm dataset as a new possible dataset to be included in the underlying empirical dataset layer of the IRI model. The results show that the application of the Lomidze correction improved the agreement with ISR data above all at mid latitudes and during daytime, and it was effective in reducing the mismatch between Swarm and IRI <i>T</i>_e values. This suggests that future developments of the IRI <i>T</i>_e model should include the Swarm dataset with the Lomidze correction. However, the existence of a quasi-linear relation between measured and modeled <i>T</i>_e values was well verified only below about 2200 K, while for higher values it was completely lost. This is an important result that IRI <i>T</i>_e model developers should properly consider when using the Swarm dataset.