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Patagonia is the coldest of these deserts and the one furthest away from the tropics. This is the answer to your question.

Patagonian Desert.

It is because of the quirky nature of the South American continent's alignment with respect to the Ocean. Formation of a desert is due to the Ocean currents. In mid (25° to 40°) latitudes there is an upwelling of Cold (subsurface) current that comes from a Pole, on the Western coastal margin of the continent. In the case of South America with its long and pointed southern tip, the circumpolar (cold subsurface) current splits up with the main branch washing the eastern margin (Patagonia) of the continent instead of curling back to join the Circumpolar current, while upwelling near the Atacama desert (as usual) on the West coast.