An apparatus, comprising: a catheter arrangement comprising a flexible shaft; a balloon disposed at a distal end of the shaft and configurable for deployment within a target vessel of the body; a plurality of ablation electrodes supported by a wall of the balloon, the ablation electrodes configured to deliver electrical energy sufficient to ablate target tissue proximate a wall of the target vessel when the balloon is in a deployed configuration; and a cooling arrangement encompassed at least in part by the balloon and configured to provide cooling to at least the electrodes during ablation such that a location at which steady-state ablative heating begins is translated from an electrode-tissue interface at the target vessel wall to a location a predetermined distance away from the electrode-tissue interface, wherein the cooling arrangement comprises: a phase-change cryothermal apparatus configured to receive a liquid cooling media and output spent gas resulting from the cryothermal phase-change; or a heat exchange apparatus configured to receive a cooled liquid cooling media and output spent liquid cooling media; or one or more solid-state thermoelectric cooling devices; and wherein the apparatus further comprises an electrical conductor extending along the shaft and arranged to be in electrical communication with a conductive fluid within the balloon, such that the electrodes can be energized by the conductive fluid. a catheter arrangement comprising a flexible shaft; a balloon disposed at a distal end of the shaft and configurable for deployment within a target vessel of the body; a plurality of ablation electrodes supported by a wall of the balloon, the ablation electrodes configured to deliver electrical energy sufficient to ablate target tissue proximate a wall of the target vessel when the balloon is in a deployed configuration; and a cooling arrangement encompassed at least in part by the balloon and configured to provide cooling to at least the electrodes during ablation such that a location at which steady-state ablative heating begins is translated from an electrode-tissue interface at the target vessel wall to a location a predetermined distance away from the electrode-tissue interface, wherein the cooling arrangement comprises: a phase-change cryothermal apparatus configured to receive a liquid cooling media and output spent gas resulting from the cryothermal phase-change; or a heat exchange apparatus configured to receive a cooled liquid cooling media and output spent liquid cooling media; or one or more solid-state thermoelectric cooling devices; and wherein the apparatus further comprises an electrical conductor extending along the shaft and arranged to be in electrical communication with a conductive fluid within the balloon, such that the electrodes can be energized by the conductive fluid. a phase-change cryothermal apparatus configured to receive a liquid cooling media and output spent gas resulting from the cryothermal phase-change; or a heat exchange apparatus configured to receive a cooled liquid cooling media and output spent liquid cooling media; or one or more solid-state thermoelectric cooling devices; and wherein the apparatus further comprises an electrical conductor extending along the shaft and arranged to be in electrical communication with a conductive fluid within the balloon, such that the electrodes can be energized by the conductive fluid.