Membrane distillation is an attractive technology for production of fresh water from seawater. The MemPower®MemPower® concept, studied in this work, uses available heat (86 °C) to produce pressurized water (2.2 bar and 46 °C) by membrane distillation, which again can be used to power a turbine for co-production of electricity. We develop a non-equilibrium thermodynamic model to accurately describe the transfer at the liquid-membrane interfaces, as well as through the hydrophobic membrane. The model can explain the observed mass flux, and shows that 85% of the energy is dissipated at the membrane-permeate interface. It appears that the system's performance will benefit from a lower interface resistance to heat transfer, in particular at the permeate side of the membrane. The nature of the membrane polymer and the pore diameter may play a role in this context.