In recent years, phononic crystals have emerged as a possible route for engineering the thermal properties of semiconductor materials like silicon independently of their electronic properties. Heat carriers, or thermal phonons, in Si are very difficult to manipulate due to their wide range of frequencies and nanoscale size. Nanostructures are required to most effectively manipulate thermal phonons, but are extremely difficult to fabricate due to resolution limitations of modern lithography equipment. We present in this work several different block-copolymer nanolithography-based approaches for fabricating sub-resolution limit hexagonal arrays of holes at a pitch of 37.5 nm with an overall porosity of ~42% in Si materials that functioned as phononic crystals. In addition to fabrication details, thermal conductivity measurements are presented for several Si-based phononic crystals and a prototypical phononic crystal-enhanced IR sensor. The overall theme of this work was to expand the experimental understanding of low-dimensional thermal phonon transport in nanostructured materials, with an emphasis on probing the roles of incoherent and coherent scattering, and diffusive and ballistic transport under ambient conditions. We demonstrate that Si nanostructures templated by block-copolymer nanolithography effectively function as phononic crystals capable of reducing the thermal conductivity by 80-90% relative to bulk. We also demonstrate that the orientation of nanostructures with respect to the direction of heat flow at these length scales has a measurable effect on the thermal conductivity.