Coronal-Line Forest Active Galactic Nuclei (CLiF AGN) are characterized by strong, high-ionization lines, which are in contrast to what is found in typical AGNs. Here, we carry out an infrared analysis aimed at understanding the spectral energy distribution (SED) of six sources from this group. In this work, the properties of the dusty torus for these objects are analysed. To this purpose, we infer the physical and geometrical properties of the dust structure that surrounds the central region by fitting with models, the SED of CLiF AGNs in the infrared. For this analysis, we compare the results of three models: CLUMPY, SKIRTOR, and CAT3D-WIND. Using the Bayesian information criterion, SKIRTOR was found to have the most robust fit to the SEDs in five out of six galaxies. The remaining object was best fitted with CLUMPY. The results indicate that these objects are preferentially Type I sources, supporting the detection of broad components in the permitted lines, likely associated with the broad-line region in the near-infrared spectra. The best SED fitting indicates that the line of sight gives access to the view of the central source for these objects, but the amount of dusty clouds in the same direction is high, suggesting the hypothesis that they obscure the emission of the continuum produced by the central source and that the obscuration makes the coronal lines to not overlap with the continuum.