Global Navigation Satellite Systems (GNSS) radio occultations allow the vertical sounding of the Earth's atmosphere, in particular, the ionosphere. The physical observables estimated with this technique permit to test theoretical models of the electron density such as, for example, the Chapman and the Vary‐Chap models. The former is characterized by a constant scale height, whereas the latter considers a more general function of the scale height with respect to height. We propose to investigate the feasibility of the Vary‐Chap model where the scale height varies linearly with respect to height. In order to test this hypothesis, the scale height data provided by radio occultations from a receiver on board a low Earth orbit (LEO) satellite, obtained by iterating with a local Chapman model at every point of the topside F2 layer provided by the GNSS satellite occultation, are fitted to height data by means of a linear least squares fit (LLS). Results, based on FORMOSAT‐3/COSMIC GPS occultation data inverted by means of the Improved Abel transform inversion technique (which takes into account the horizontal electron content gradients) show that the scale height presents a more clear linear trend above the F2 layer peak height, hm, which is in good agreement with the expected linear temperature dependence. Moreover, the parameters of the linear fit obtained during four representative days for all seasons, depend significantly on local time and latitude, strongly suggesting that this approach can significantly contribute to build realistic models of the electron density directly derived from GNSS occultation data.