Cooling apparatuses and coolant-cooled electronic assemblies are provided which include a thermal transfer structure configured to couple to one or more sides of an electronics card having one or more electronic components to be cooled. The thermal transfer structure includes a thermal spreader coupled to the one side of the electronics card, and the apparatus further includes a coolant-cooled structure disposed adjacent to the socket of the electronic system. The coolant-cooled structure includes: one or more low-profile cold rails sized and configured to thermally couple to the thermal spreader along a bottom edge of the thermal spreader with operative docking of the electronics card within the socket; and one or more coolant-carrying channels associated with the low-profile cold rail(s) for removing heat from the low-profile cold rail(s) to coolant flowing through the coolant-carrying channel(s).