In this paper we discuss the issues of the equilibration dynamics of spatially indirect two-dimensional excitons in a coupled quantum well structure, in particular those trapped by an in-plane harmonic potential trap. We discuss the relative timescales for several processes. In the experiments with an in-plane trap, we can use the size of the exciton cloud as a measure of the temperature of particles. At low lattice temperatures the exciton temperature is higher than that of the lattice, even long after equilibrium has obviously been reached. We discuss the effects that can be responsible for this.