The variation in the high energy cut-off E_c in active galactic nuclei uniquely probes the corona physics. In this work we show that the ratio of two NuSTAR spectra (in analogy to difference imaging technique widely used in astronomy) is uniquely useful in studying E_c variations. The spectra ratio could directly illustrate potential E_c variation between two spectra. By comparing with the ratio of two spectral fitting models, it also examines the reliability of the spectral-fitting measured E_c variation. Assisted with this technique, we revisit the 5 AGNs in literature (MCG -5-23-16, 3C 382, NGC 4593, NGC 5548 and Mrk 335) for which E_c (kT_e) variations have been claimed with NuSTAR observations. We show the claimed E_c variations appear inconsistent with the spectra ratios in three of them, thus need to be revised, demonstrating the striking usefulness of spectra ratio. We present thereby improved spectral fitting results and E_c variations. We also report a new source with E_c variations based on NuSTAR observations (radio galaxy 4C +74.26). We find the corona tends to be hotter when it brightens (hotter-when-brighter) in 3C 382, NGC 5548, Mrk 335 and 4C +74.27, but MCG -5-23-16 and NGC 4593 show no evidence of significant E_c variations. Meanwhile all 6 sources in this small sample appear softer-when-brighter. Changes in corona geometry are required to explain the observed hotter-when-brighter trends.
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