A solid-state cooling principle based on magnetic-field-driven tunable suppression of Andreev reflection in superconductor/two-dimensional electron gas nanostructures is proposed. This cooling mechanism can lead to very large heat fluxes per channel up to 10;{4} times greater than currently achieved with superconducting tunnel junctions. This efficacy and its availability in a two-dimensional electron system make this method of particular relevance for the implementation of quantum nanostructures operating at cryogenic temperatures.