A main challenge in colloid science is the development of smart delivery systems that store and protect actives from degradation and allow release in response to an external stimulus like temperature. Hollow nanogel capsules made of temperature-sensitive polymers are particularly promising materials. The stimuli-sensitive void size, shell thickness, and permeability determine cargo storage and its release behavior. Thus, determination and control of these morphological parameters are of outmost relevance for the design of new, functional drug delivery vehicles. Here we investigate quantitatively void size and shell thickness of hollow nanogels at different states of swelling by means of small-angle neutron scattering (SANS) employing contrast variation. We demonstrate the structure-sensitivity dilemma: hollow nanogels with a slightly cross-linked shell reveal distinct temperature sensitivity but possess nearly no void (14% of the initial core volume) and are thus hardly hollow. Nanogels with a stiff shell are indeed hollow (albeit with smaller void as compared to the core size of the template) but less temperature sensitive.