We use a simplified model of convection in a porous medium to investigate the balances of mass and energy within a subseafloor hydrothermal convection cell. These balances control the steady state structure of the system and allow scalings for the height, permeability, and residence time of the “reaction zone” at the base of the cell to be calculated. The scalings are presented as functions of (1) the temperature TD of the heat source driving the convection and (2) the total power output ΦU. The model is then used to illustrate how the nonlinear thermodynamic properties of water may impose the observed upper limit of ∼400°C on vent temperatures. The properties of water at hydrothermal conditions are contrasted with those of a hypothetical “Boussinesq fluid” for which temperature variations in fluid properties are either linearized or ignored. At hydrothermal pressures, water transports a maximum amount of energy by buoyancy‐driven advection at ∼400°C. This maximum is a consequence of the nonlinear thermodynamic properties of water and does not arise for a simple Boussinesq fluid. Inspired by the “Malkus hypothesis” and by recent work on dissipative systems, we speculate that convection cells in porous media attain a steady state in which the upwelling temperature TU maximizes the total power output of the cell. If true, this principle would explain our observation (in previous numerical simulations) that water in hydrothermal convection cells upwells at TU ∼ 400°C when driven by a heat source above ∼500°C.