Flexible and compressible temperature sensors are highly desired for artificial skin and epidermal electronics. Here we demonstrated a flexible and compressible resistive temperature sensor using hierarchically buckled carbon nanotube/rubber bi-sheath-core structure (a buckled carbon nanotube outer sheath and a buckled rubber inner sheath wrapped around a rubber fiber core). When heated, lateral contacts of the adjacent buckles increase, resulting in electrical resistance decrease and serving as highly sensitive temperature sensors. This bi-sheath-core fiber temperature sensor showed high linearity, good repeatability, large negative temperature coefficient of resistance (NTC = -54.7/°C), and insensitivity to compressive deformations (up to -20% strain). The NTC and temperature dependence of percent resistance change can be easily tuned by modulating the buckling bi-sheath-core structures such as varying the number of nanotube layers and the rubber sheath stiffness.