We analyze the interaction between dark energy and dark matter from a thermodynamical perspective. By assuming they have different temperatures, we study the possibility of occurring a decay from dark matter into dark energy, characterized by a negative parameter $Q$. We find that, if at least one of the fluids has nonvanishing chemical potential, for instance ${\ensuremath{\mu}}_{x}<0$ and ${\ensuremath{\mu}}_{\mathrm{dm}}=0$ or ${\ensuremath{\mu}}_{x}=0$ and ${\ensuremath{\mu}}_{\mathrm{dm}}>0$, the decay is possible, where ${\ensuremath{\mu}}_{x}$ and ${\ensuremath{\mu}}_{\mathrm{dm}}$ are the chemical potentials of dark energy and dark matter, respectively. Using recent cosmological data, we find that, for a fairly simple interaction, the dark matter decay is favored with a probability of $\ensuremath{\sim}93%$ over the dark energy decay. This result comes from a likelihood analysis where only background evolution has been considered.