We perform an analysis of the supercooled state in an analogue of an early universe phase transition based on a one dimensional, two-component Bose gas with time-dependent interactions. We demonstrate that the system behaves in the same way as a thermal, relativistic Bose gas undergoing a first order phase transition. We propose a way to prepare the state of the system in the metastable phase as an analogue to supercooling in the early universe. While we show that parametric resonances in the system can be suppressed by thermal damping, we find that the theoretically estimated thermal damping in our model is too weak to suppress the resonances for realistic experimental parameters. However, we propose that experiments to investigate the effective damping rate in experiments would be worthwhile.