The performance potential of a heat pipe designed specifically to operate in the high magnetic fields of a fusion reactor is investigated analytically. The heat pipe has a thin, flat cross section aligned parallel to the magnetic field so as to reduce the eddy currents and the resultant magnetohydrodynamic pressure drops in the liquid wick flow. The flat heat pipes are used to cool a pool of liquid lithium (or lithium-lead eutectic) in the blanket that surrounds the central-cell plasma of a tandem mirror fusion reactor. Calculations indicate that this new heat pipe design may be able to transport up to ∼6800 W/cm2 of condenser cross-sectional area in a 2-T magnetic field. This is considerably higher than the 420 W/cm2 capability of a conventional cylindrical heat pipe of similar dimensions employing a channel wick and operating in the same 2-T field.