Yes / Multieffect distillation with thermal vapour compression (MED–TVC) is one of the most attractive thermal desalination technologies for the production of freshwater. Several mathematical models were presented in the open literature to analyse the steady-state performance of such process. However, these models have several limitations and assumptions. Therefore, there remains the challenge of having a reliable model to accurately predict the performance of the MED process. Thus, this research attempts to resolve this challenge by rectifying the shortcomings of the models found in the literature and create a new one. The robustness of the developed model is evaluated against the actual data of Umm Al-Nar commercial plant situated in UAE. In seawater desalinisation, a large amount of high-salinity stream (brine) is rejected back into the sea. This paper investigates the influence of the rejected (exit) brine temperature on the system performance parameters of MED–TVC process. Specifically, these parameters are considered as total heat consumption, gain output ratio, freshwater production, heat transfer area and performance ratio. Also, the particular parameters of TVC section of the entrainment ratio, compression ratio and expansion ratio are also addressed. Moreover, a critical evaluation of the influence of the rejected brine temperature on the seawater is also embedded.