Depletion interactions between colloids of discoidal shape can induce their self-assembly into columnar aggregates. This is an effect of entropic origin with important implications in a range of colloidal systems, particularly in the clustering of erythrocytes that determine the rheological properties of blood. Here, we investigate the equilibrium state reached by discoidal colloids in a solution of smaller depletant particles. We develop a thermodynamic model of depletion-induced aggregation based on self-assembly theory and solve it analytically. We test the validity of the model by using Langevin simulations of a system of discs and depletant particles in which the depletion interaction emerges naturally. In addition, we consider the effect of an attractive interaction between depletant and discoidal particles, which we show induces a re-entrant dependence of aggregation with temperature.