We apply the two-particle irreducible (2PI) formalism as a framework for consistent thermal resummation in studies of cosmological phase transitions (PTs). Considering a model with two real scalar fields, we work within the Hartree approximation and renormalise the 2PI effective action using an on-shell scheme, while introducing a connection to physical parameters. This yields the Hartree-resummed finite-temperature effective potential, which treats high- and low-temperature corrections on an equal footing, thereby avoiding the limitations of conventional methods based on the high-temperature approximation. With this potential, we study one- and two-step transitions within the model, computing the PT parameters (the temperature, duration, and strength of the transition), and compare our results with those obtained using resummation schemes widely employed in the literature. Finally, using these PT parameters, we evaluate the gravitational wave spectrum generated from first-order PTs, demonstrating the impact of the choice of resummation scheme on the spectrum.