The robust T ∝ nδ power-law relationship between the temperature (T) and the density (n) that arises during the radiative cooling phase of a solar coronal loop is investigated. Using an analytical model and numerical hydrodynamic simulations, we demonstrate that radiative energy loss from the transition region is the dominant physical process. It governs the down-flow by which mass is lost from the corona and hence controls the evolution of the entire loop. We also show that the down-flow is initiated by a weakening of the pressure gradient between the corona and the transition region, such that the plasma can no longer be supported in hydrostatic equilibrium. Rather than driving the down-flow, the pressure gradient actually regulates it and acts as a brake against gravitational acceleration.