2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/215659We discuss the thermodynamic properties of the Friedmann-Robertson-Walker universe with dark energy fluids labelled by $ω=p/ρ<-1/3$. Using the integrability condition, we show that the phantom phase of $w<-1$ can still be thermodynamically allowed even when the temperature takes on negative values because in that case, there exists at least a condition of keeping physical values for $p$ and $ρ$8 pages, 1figure, title changed, version to appear in PLBGeneral Relativity and Quantum Cosmologytext