Liquid heat exchangers and methods for removing heat from a central processing unit. An exemplary heat exchanger comprises a body having an open cavity whose periphery is sealable to the central processing unit from which heat is to be removed, a cooling liquid inlet port coupled through the body to the open cavity, and a liquid outlet port coupled through the body to the open cavity. Cooling liquid is pumped through the cavity when the body is sealed to the central processing unit, thereby contacting the central processing unit and removing heat from the central processing unit. A plurality of heat conducting elements may be provided that extend from an inner surface of the body into the open cavity, at least some of which have a length that is operative to contact the central processing unit. The heat conducting elements allow convective cooling of the central processing unit.