Swelling properties of doubly temperature sensitive core-shell microgels consisting of two thermosensitive polymers with lower critical solution temperatures (LCTS) at, respectively, 34 degrees C in the core and 44 degrees C in the shell have been investigated by small-angle neutron scattering (SANS). A core-shell form factor has been employed to evaluate the structure, and the real space particle structure is expressed by radial density profiles. By this means, the influences of both shell/core mass composition and shell cross-linker content on the internal structure have been revealed at temperatures above, between, and below the LCSTs. Higher shell/core mass ratios lead to an increased expansion of the core at temperatures between the LCSTs, whereas a variation of cross-linker in the shell mainly effects the dimensions of the shell. The influence on the core structure was interpreted as resulting from an elastic force developed from the swollen shell. At temperatures below the core LCST, the core cannot swell to its native size (i.e., in the absence of a shell), because the maximum expanded shell network prohibits further swelling. Thus, depending on temperature, the shell either expands or compresses the core.