Convective flow through a porous medium in a rectangular vessel with a linear temperature profile steadily maintained on the boundary is investigated. On the basis of numerical experiments the realization of steady regimes that belong to a globally stable, one-parameter family is studied at different vessel dimensions and initial temperature distributions. The regime selection is shown to strongly depend on the initial fluid temperature: a vicinity of two regimes is realized from initial data similar with the state of rest; at high initial fluid heating the regimes are selected from a vicinity of two other regimes; and in intermediate situations any of infinite number of steady regimes can be attained.