A drinkware container system includes a container body having an outer wall and an inner wall spaced from the outer wall to define a cavity. The inner wall extends between an opening of the container body and a base wall. The inner wall and base wall define a chamber that receives a liquid, the bottom wall spaced below the base wall. A cold-side heat sink is located in the cavity in thermal contact with the inner wall and/or the base wall. Optionally, a phase change material is located in the cavity and in thermal communication with the chamber and with the cold side heat sink, the phase change material spaced apart from the outer wall. The cavity can optionally be filled with an insulation material or be under vacuum. Optionally, the container body can have magnet(s) that can removably couple it with a cooling unit. The cooling unit can have a first heat sink configured to contact the container body when the container body is placed on the cooling unit, thermoelectric module(s) in thermal communication with the first heat sink, and a second heat sink in thermal communication with the thermoelectric module(s) so that the thermoelectric module(s) are interposed between the first and second heat sinks. The thermoelectric module(s) are operable to draw heat from the first heat sink and transfer it to the second heat sink to cool the first heat sink to thereby draw heat from the container body to cool it.