  We investigate the non-zero temperature dynamics of a sub-GeV dark matter
scenario freezing-out via self-interactions. As a prototype, we take up the
case of a scalar dark matter species undergoing $3 \to 2$ number changing
annihilations catalysed by another scalar. We study the shape of the thermal
potential of this scenario in a parameter region accounting for the observed
relic abundance. An analysis reveals the possibility of a first order phase
transition with bubble nucleation occurring at sub-GeV temperatures. This
finding can be correlated with the typical sub-GeV masses in the framework. The
gravitational wave spectra associated with such a phase transition is
subsequently computed.
