Low-temperature RF switches are key components in superconducting microwave circuits, quantum measurements, and cryogenic electronics systems. This is because that the traditional semiconductor RF switches usually fail at low temperatures, due to the carrier freeze-out effect, making them diffcult to be directly applied in superconducting microwave environments. In this work, we propose and experimentally demonstrate a low-temperature RF switch, based on a distributed half-wavelength superconducting coplanar waveguide resonator for generating a superconducting Fano device. By taking advantage of the temperature sensitivity of the resonant frequency of the Fano device, we implement the temperature-controlled resonant tuning, based on the temperature-sensitive superconducting aluminum film's dynamic inductance regulation, thereby converting the sensitive thermal-induced frequency shift of the asymmetric Fano line shape into the significant microwave transmission characteristics changes. Through the establishment of a time-domain coupled mode theory, considering the intrinsic loss of the resonator, we systematically analyze the working mechanism and tunability of the low-temperature RF switch and discuss the influence of the resonator's intrinsic quality factor, coupling quality factor, and through-path scattering parameters on the peak-to-valley separation of Fano scattering spectrum and peak-to-valley contrast of the Fano scattering spectrum. We measured the microwave transmission characteristics of the aluminum-film distributed superconducting resonator in a dilution refrigerator and then characterized its temperature-sensitive Fano effect in the temperature range of 500 to 1150 millikelvins. The experimental results show that the resonant frequency of the resonator redshifts significantly with the increase of temperature, confirming that the temperature sensitivity of the superconducting dynamic inductance can be used to achieve temperature-controlled tuning of the Fano scattering. By numerically fitting the temperature-dependent resonant frequency changes, the dynamic inductance ratio of the device was measured as approximately 1.94%; and the superconducting transition temperature of the device is about 1403.53 millikelvins. By testing the transmission characteristics of the device for a 5.87598 GHz RF signal, we demonstrated its temperature-controlled on/off state switching function, achieving the maximum extinction ratio of 33.6 dB. By taking advantage of the particularly sensitive temperature response of the device, near the superconducting transition temperature region, we demonstrated a noise equivalent temperature difference of 1.22 millikelvins at 1150 millikelvins, thereby achieving a temperature sensitivity of 0.2887 MHz/mK. This distributed superconducting resonator temperature-sensitive sensing with millikelvin-level temperature resolution does not require any additional active biasing or nonlinear component, thus can provide a feasible solution for high-precision temperature sensing measurements in the cryogenic region. In particular, it might provide a significant reference for the preparation of such highly temperature-sensitive Fano devices, using superconducting films with a transition temperature of around 50 mK, to achieve the desired real-time thermal condition monitoring on-chip for ultra-low-temperature superconducting quantum chips.