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We demonstrate fiber optic, multiplexible temperature sensing using a fiber Bragg grating (FBG) with an operational range of 2-400 K, and a temperature resolution better than 10 mK for temperatures <;12 K. This represents a significant reduction in the lowest usable temperature as well as a significant increase in sensitivity at cryogenic temperatures compared with previously reported multiplexible solutions. This is accomplished by mounting the section of the fiber with a FBG on a polytetrafluoroethylene coupon, which has a non-negligible coefficient of thermal expansion down to <;4 K. The sensors exhibit a good stability over multiple temperature cycles and acceptable sensor-to-sensor repeatability. Possible applications for this sensor include distributed temperature sensing across superconducting elements and cryogenic temperature measurements in environments where electrical measurements are …