Above the lower critical solution temperature T(c) (ca. 34 degrees C), poly(N-isopropylacrylamide) hydrogels become weakly hydrophobic and undergo microphase separation. Macroscopic deswelling, however, is extraordinarily slow, the out-of equilibrium state of the gel being conserved for many days. In this article the structure of the microphase-separated state above T(c) is probed by small-angle X-ray scattering and by pulsed field gradient NMR of the protons of water, both in the water phase and in the polymer-rich phase. Above T(c) the gel comprises two microphases, separated by smooth interfaces. The cavities occupied by the water phase form a connected network. The diffusion rate of the water molecules in this phase varies from one cavity to another and can be described by a Gaussian distribution. Water molecules belonging to the polymer-rich phase are also mobile, but their self-diffusion coefficient D is greatly diminished. Absence of compartmentalization of the water phase implies that the slow deswelling rate of the gel is not due to trapping of the water phase.