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We present evidence for strong radiative cooling in a pulsed-power-driven magnetic reconnection experiment. Two aluminum exploding wire arrays, driven by a 20 MA peak current, 300 ns rise time pulse from the Z machine (Sandia National Laboratories), generate strongly driven plasma flows (MA≈7) with anti-parallel magnetic fields, which form a reconnection layer (SL≈120) at the mid-plane. The net cooling rate far exceeds the Alfvénic transit rate (τcool−1/τA−1≫1), leading to strong cooling of the reconnection layer. We determine the advected magnetic field and flow velocity using inductive probes positioned in the inflow to the layer, and inflow ion density and temperature from analysis of visible emission spectroscopy. A sharp decrease in x-ray emission from the reconnection layer, measured using filtered diodes and time-gated x-ray imaging, provides evidence for strong cooling of the reconnection layer after its initial formation. X-ray images also show localized hotspots, regions of strong x-ray emission, with velocities comparable to the expected outflow velocity from the reconnection layer. These hotspots are consistent with plasmoids observed in 3D radiative resistive magnetohydrodynamic simulations of the experiment. X-ray spectroscopy further indicates that the hotspots have a temperature (170 eV) much higher than the bulk layer (≤75 eV) and inflow temperatures (about 2 eV) and that these hotspots generate the majority of the high-energy (>1 keV) emission.