No. The parts of the chip that conduct electricity to the active areas in current chips are already made from metal. Basic chips are made from layers of metal / oxide / semiconductor (MOS).
Current flows through silicon only in small areas, and the way chips work is that you can "turn off" the high resistivity in those areas and make them conducting (by doping the material + applying electric currents & fields)
In the presented work, an air gap is used for these "active areas" instead of a semiconductor. An air gap does have resistance, so there will be resistive heating just like in normal chips.