  The propagation of light in nonlinear media is well described by a $2$D
nonlinear Schr\"odinger equation (NLSE) within the paraxial approximation,
which is equivalent to the Gross-Pitaesvskii equation (GPE), the mean-field
description for the dynamics of Bose-Einstein condensates (BECs). Due to this
similarity, many theoretical and experimental investigations of phenomena which
have already been studied and realized in BECs have been recently analysed in
alternative experimental platforms such as hot atomic vapours. In this work, we
study the formation of droplets of light in these media, attempting to
establish a mapping between the experimental parameters normally used in BEC
experiments and those needed to observe the analogous phenomenon in hot atomic
vapours. We obtain the energy functional for the susceptibility of the medium
in the $\chi^{(3)}$ , $\chi^{(3)}+\chi^{(5)}$ and saturating regimes for a
two-level atomic configuration considering the focusing (attractive) regime. We
apply a Gaussian variational approach and check its predictions through
numerical simulations of the NLSE for each regime. Finally, we study the
real-time dynamics of the system for both the $\chi^{(3)}+\chi^{(5)}$ and
saturating nonlinearities, focusing our attention on the behaviour of the
breathing mode and on the analysis of droplet formation for realistic
experimental conditions.
