In a one-dimensional polarization-gradient cooling scheme, with two counter-propagating laser beams having mutually orthogonal linear polarization, a linear array of potential wells for cold atoms is formed. These optical potential wells are created by the spatially varying light shift of the atomic ground state. Transitions between quantized vibrational states in such wells have been observed by stimulated and spontaneous Raman spectroscopy. Recently, this was extended to three dimensions using both four beams and six beams. In this work, we intersect four travelling-wave laser beams, all polarized in the same plane. This produces a three-dimensional body-centered cubic lattice of potential wells for cesium atoms. We have used fluorescence spectroscopy to measure the temperature and the localization of the atoms, with the temperature as low as 2 μK and the localization about λ/20 rms. We utilize this localization to further cool the atoms by reducing the intensities slowly, thereby reducing the steepness of the potential wells slowly enough to allow the atomic spatial distribution to expand adiabatically. When measuring the temperature of the atoms at different time delays after beginning to decrease the depth of the potential, we find that after 100-300 μs the atoms are cooled to velocities corresponding to less than 700 nK in all directions.