Solid-state refrigeration represents a promising alternative to vapor compression refrigeration systems which are inefficient, unreliable, and have a high global warming potential. However, several solid-state cooling technologies—including those relying on a temperature change induced by an applied electric field (electrocaloric effect), magnetic field (magnetocaloric effect), and uniaxial stress (elastocaloric effect)—have been investigated, but their efficiency and scalability remain a concern. Materials with a large barocaloric response—temperature/entropy change induced by hydrostatic pressure—hold a significant promise for solid-state cooling but remain comparatively less explored. These materials need to be inexpensive, compressible, and show a large barocaloric response around the temperature of interest. Soft materials have the potential to meet these requirements and enable the development of low-cost high-efficiency solid-state heat pumps. Here, we investigate the barocaloric performance of commercially available block copolymer thermoplastic elastomers. We characterized the mechanical, thermal, and barocaloric properties of these materials and evaluated their potential for solid-state refrigeration. We utilized rheometric measurements to evaluate the isothermal compressibility and normalized refrigerant capacity of the thermoplastic elastomers. In addition, we directly measured the pressure-induced temperature change of the test materials and compared them with their normalized refrigeration capacity. The measured isothermal compressibility was in the 0.1–0.4 GPa−1 range, while the normalized refrigeration capacity varied between 13.2 and 41.9 kJ K−1 GPa−1 for a 100 MPa applied pressure and 65°C temperature span. The corresponding pressure-induced temperature change for an applied pressure of 434.1 MPa varied between 2.2 and 28°C. These results demonstrated the superior barocaloric properties of thermoplastic elastomers and their promise for next generation barocaloric solid-state refrigeration devices.