This paper presents the electrothermal analysis of the performances of a Power Delivery Network for nanoscale integrated circuits, comparing standard (copper) with carbon nanotubes and graphene interconnects. Realistic carbon interconnects are considered, with the typical values of electrical and thermal parameters obtainable with the current fabrication technology. A temperature-dependent model for the electrical resistance is adopted, able to describe the case of negative temperature coefficient of the resistance, as it has been theoretically predicted and experimentally proved. The electrothermal analysis of the power network of a standard chip puts on evidence, for the first time, an interesting trade-off between voltage drop and temperature increase, while exploiting carbon nanotube and graphene based interconnects.