The Non-Inertive-Feedback Thermofluidic Engine (NIFTE) is a two-phase thermofluidic oscillator which, by means of persistent periodic thermal-fluid oscillations when placed across a steady temperature difference, is capable of utilising low-grade (i.e. low temperature) heat to induce a fluid motion. Two linearised models of the NIFTE are presented in this paper, both containing a description of the phase-change convective heat transfer that takes place between the working fluid and the heat exchangers. The first model (LTP) imposes a steady linear temperature profile along the surface of the heat exchangers; and the second (DHX) allows the solid heat exchanger blocks to store and release heat dynamically as they interact thermally with the working fluid. In earlier work [Solanki et al., Applied Thermal Engineering, 2012] it was found that these models predict the oscillation (i.e. operation) frequency of an existing NIFTE prototype pump well, but overestimate its reported efficiency. Specifically, the LTP and DHX models predicted exegetic efficiencies 11 and 30 times higher than those observed experimentally, respectively. In the present paper, a dissipative thermal loss parameter that can account for the exergetic losses due to the parasitic, cyclic phase change and heat exchange within the device is included in both models in an effort to make realistic predictions of the exergetic efficiencies. The LTP and DHX models, including and excluding the thermal loss parameter, are compared to experimental data. It is found that the inclusion of the thermal loss parameter increases the predicted oscillation frequencies in the DHX model, but has a negligible effect on the frequencies predicted by the LTP model. A more significant effect is observed on the exergetic efficiencies, whereby the inclusion of the thermal loss parameter leads to a greatly improved prediction by both the LTP and DHX models, both in trend and approximate magnitude, of the exergetic efficiency of the prototype NIFTE pump. From the results it is concluded that, on accounting for thermal losses, the DHX model achieves the best predictions of the key performance indicators of the NIFTE, that is, of the oscillation frequency and exergetic efficiency of the device.