Dark energy in thermal equilibrium with the cosmological horizon?

According to a generalization of black hole thermodynamics to a cosmological framework, it is possible to define a temperature for the cosmological horizon. The hypothesis of thermal equilibrium between the dark energy and the horizon has been considered by many authors. We find the restrictions imposed by this hypothesis on the energy transfer rate ($Q_i$) between the cosmological fluids, assuming that the temperature of the horizon have the form $T=b/2\pi R$, where $R$ is the radius of the horizon. We more specifically consider two types of dark energy: holographic dark energy (HDE) and dark energy with a constant EoS parameter ($w$DE). In each case, we show that for a given radius $R$, there is an unique term $Q_{de}$ that is consistent with thermal equilibrium. We also consider the situation where, in addition to dark energy, other fluids (cold matter, radiation) are in thermal equilibrium with the horizon. We find that the interaction terms required for this will generally violate energy conservation ($\sum_i Q_i=0$).