The internal structure of nanometric microgels in water has been studied as a function of temperature, cross-linker content, and level of deuteration. Small-angle neutron scattering from poly(N-isopropylmethacrylamide) (volume phase transition approximate to 44 degrees C) microgel particles of radius well below 100 nm in D2O has been measured. The intensities have been analyzed with a combination of polymer chain scattering and form-free radial monomer volume fraction profiles defined over spherical shells, taking polydispersity in size of the particles determined by atomic force microscopy into account. A reverse Monte Carlo optimization using a limited number of parameters was developed to obtain smoothly decaying profiles in agreement with the experimentally scattered intensities. The results are compared to the swelling curve of microgel particles in the temperature range from 15 to 55 degrees C obtained from photon correlation spectroscopy (PCS). In addition to hydrodynamic radii measured by PCS, our analysis provides direct information about the internal water content and gradients, the strongly varying steepness of the density profile at the particle-water interface, the total spatial extension of the particles, and the visibility of chains. The model has also been applied to a variation of the cross-linker content, N,N'-methylenebisacrylamide, from 5 to 15 mol %, providing insight on the impact of chain architecture and cross-linking on water uptake and on the definition of the polymer-water interface. The model can easily be generalized to arbitrary monomer contents and types, in particular mixtures of hydrogenated and deuterated species, paving the way to detailed studies of monomer distributions inside more complex microgels, in particular core-shell particles.