A fiber-optic extrinsic Fabry–Perot interferometric (EFPI) temperature sensor with extremely high resolution and large dynamic range is proposed and demonstrated. The sensor uses a thermally expanded core (TEC) fiber as the first reflective surface of the interference cavity to focus the beam to improve the finesse of the interference fringes, which enables extremely high cavity length resolution and large dynamic range with a multivalley averaging method based on dynamic estimation of the fringe order. Using a borosilicate capillary as the temperature-sensitizing material, a cavity length sensitivity of 79.25 nm/°C as well as a good linearity were obtained in the temperature range of 10 °C–100 °C. A temperature resolution of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$7.5\times 10^{-{5}}\,\,^{\circ }\text{C}$ </tex-math></inline-formula> was demonstrated. The extremely high-temperature resolution with a large dynamic range has an important application value in the monitoring of weak temperature changes in deep sea and underground fluids.