An ice maker includes a mold body. A plurality of mold cavities are defined in the mold body. Each mold cavity extends between a floor and an opening along a longitudinal axis. Each mold cavity is enclosed by at least one sidewall between the floor and the opening. The longitudinal axis of each mold cavity is oriented generally along the vertical direction. The ice maker also includes a heater in thermal communication with the floor of each mold cavity of the plurality of mold cavities. The heater is configured to maintain water within a lower portion of each mold cavity in a liquid state. The ice maker further includes a drain conduit in fluid communication with the mold body and configured to receive a flow of liquid water from the mold cavities. A related refrigerator appliance and related methods are also provided.