<p>In living cells, a complex mixture of biomolecules is assembled within and across membranes. This non-equilibrium state is maintained by sophisticated protein machinery, which imports food molecules, removes waste products and orchestrates cell division. However, it remains unclear how this complex cellular machinery emerged and evolved. Here we show how the molecular contents of a cell can be coupled in a coordinated way to non-equilibrium heat flow. A temperature difference across a water-filled pore assembled the core components of a modern cell, which could then activate the gene expression. The mechanism arose from the interplay of convection and thermophoresis, both driven by the same heat source. The cellular machinery of protein synthesis from DNA via RNA was triggered as a direct result of the concentration of cell components. The same non-equilibrium setting continued to attract food molecules from an adjacent fluid stream, keeping the cellular molecules in a confined pocket protected against diffusion. Our results show how a simple non-equilibrium physical process can assemble the many different molecules of a cell and trigger its basic functions. The framework provides a membrane-free environment to bridge the long evolutionary times from an RNA world to a protein-based cell-like proto-metabolism.</p>