Small-angle neutron scattering data from a thermosensitive copolymer microgel consisting of N-isopropylacrylamide (PNIPAM) and N-isopropylmethacrylamide (PNIPMAM regions) were analyzed using a new form factor model. The neutron scattering data display an exceptional shape of the scattering curve at the transition temperature of the microgel indicating an additional characteristic length scale inside the microgel. A new form factor model with a nanophase separated internal morphology was derived which describes the experimental scattering very well. At the transition temperature of the copolymer, which is in between the transition temperatures of the two components, the copolymer microgel particles consist of collapsed PNIPAM domains and swollen PNIPMAM regions. The results demonstrate that a one-pot synthesis can lead to a highly sophisticated material with phase separated domains on a microscopic length scale.