We present a self-similar three-dimensional and spherically symmetric fluid model of the expansion of an either globally neutral or globally charged collisionless plasma into vacuum. As in previous works by other authors the key parameter of the model is the ratio of the electron Debye length to the radius R of the expanding ion sphere. The main difference with respect to the recently published model of Murakami and Basko (2006 Phys. Plasmas 13 2105) is that the electron temperature is spatially non-uniform. The major consequence of the spatial variability is that the self-similar solution is characterized by the presence of a sharp electron front at some finite distance ahead of the ion front. Explicit analytic expressions for the self-similar profiles of the ion and electron densities, the electron temperature and the heat flux are given for the region inside the ion front. The model is shown to be in good qualitative agreement with results from ab initio plasma simulations.