When a current is involved, as in spark plasma sintering, metallic powders are heated by the Joule effect through both tool and specimen. Other mechanisms might occur, but it is difficult to separate the role of the temperature from the role of the current inside the sample as, in most cases, the two parameters are not controlled independently. In this paper, the consolidation and the densification of a pure copper powder were studied in three configurations for obtaining different electric current paths: (i) current flowing through both the powder and the die, (ii) current forced into the powder and (iii) no current allowed in the powder. Electrical conductivity measurements showed that even low-density samples displayed higher conductivities than graphite by several orders of magnitude. FEM simulations confirmed that these copper specimens were mainly heated by the graphite punches. No modification of the microstructure by the flow of current could be observed. However, the absence of current in the specimen led to a decrease in densification. No significant temperature difference was modeled between the configurations, suggesting that differences are not linked to a thermal cause but rather to a current effect.