Xylem embolism is a significant factor in tree mortality. Restoration of hydraulic conductivity after massive embolisation of the vascular system requires the application of positive pressure to the vessels and/or the creation of new conductive elements. Some species generate positive pressure from the root system to propagate pressure in distal, aboveground, organs in spring, whereas other species generate positive pressure locally at the stem level during winter. We provide a mechanistic explanation for winter stem pressure build-up in the walnut tree. We have developed a physical model that accounts for temperature fluctuations and phase transitions. This model is based on the exchange of water and sugars between living cells and vessels. Our computations demonstrate that vessel pressurization can be attributed to the transfer of water between vessels across the parenchyma rays, which is facilitated by a radial imbalance in sugar concentration. The ability to dispose of soluble sugars in living cells, and to transport them between living cells and up to the vessels, are identified as the main drivers of stem pressure build-up in the walnut tree.