Resilient cores preferably for inflatable bodies having resilient slabs that define a plurality of generally columnar holes or resilient arrays of generally columnar solids. The cores further include thermal transmission mitigation materials or treatments means for improving a core's resistance to heat transfer beyond the core's innate insulative properties. Non-exclusive and non-exhaustive examples of such thermal transmission mitigation materials or treatments in slab core embodiments include consideration to hole or bore geometric cross section, frequency, pattern and orientation, the introduction of a thermal barrier at or within at least some holes or bores, and/or slab material selection/treatment. Non-exclusive and non-exhaustive examples of such thermal transmission mitigation materials or treatments in array core embodiments include consideration to the geometric cross section, frequency (density), pattern and orientation of the solids, the introduction of thermal barriers within inter-solid spaces and/or solid material selection treatment.