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We present experimental demonstration that the thermal unstability grows with reducing the width of Pt/CoFe/Pt nanowires on the way to the superparamagnetic transition. The magnetic hysteresis loops measured at room temperature using a magneto-optical Kerr effect system reveal that the coercive field decreases drastically when the nanowire width is reduced smaller than 160 nm. To understand the origin of the coercive field reduction, the coercive field is measured with varying the sweep rate of the external magnetic field and then, analyzed with a thermally-activated magnetization reversal model. It is revealed that the reduction of the coercive field is mainly ascribed to the decrement of the thermal stability parameter, which in turn induces the abrupt reduction of the retention time down to a few seconds.