The criterion of intrinsic thermal stability (ITS) of thin‐film superconductors predicts under which circumstances a thermal disturbance causes Joule heating. In the characterization method of low‐temperature scanning electron microscopy (LTSEM), the absorption of the electron beam results in a well‐controlled thermal disturbance. This work applies the ITS criterion to LTSEM of both high‐Tcand low‐Tcthin‐film superconductors and predicts the conditions for which no voltage appears along the film. The analysis of the temperature field for high‐Tcfilms differs from that for low‐Tcfilms by the absence of the acoustic‐mismatch thermal resistance between film and substrate at liquid‐nitrogen temperature. The theoretical results for low‐Tcfilms are in very good agreement with experimental data for LTSEM of lead films on sapphire substrates at 4.2 K.