1. Make the edge of the disc rub against a low friction, spring-loaded compressing element (similar to commutator brushes, but designed to really transfer a large load). This is probably infeasible because friction would eat more energy than your cycle would move.
2. Have electric actuators that are mounted on the disk itself. These would have to be powered by slip rings via the shaft. These would be active for half of the cycle and inactive for the other half. Not sure whether they should be radial, azimuthal, or axial mounted. Seems kludgey.
3. Have the disk pass through a magnetic field, exploiting the magnetic effects the article mentions. I have no idea of any of the implementation details of this, but it sounds like a better idea than 1 or 2...
If you want to cool, you pump heat outside by stopping the water cycle when the material is cold, thus allowing the water to dump it's heat into it.
If you want to heat, you pump heat inside by stopping the water cycle when the material is hot, thus allowing the water to absorb the heat from the material.
You can increase the efficiency of this by having more water touch bot the inside and outside phases (increase material surface area in contact with water and increase surface area of water cycle heatsink).
If you want to allow sub-zero temperatures, add anti-freeze to the water.