Cross-sensitivity (crosstalk) to multiple parameters is a serious but common issue for most sensors and can significantly decrease the usefulness and detection accuracy of sensors. In this work, a high sensitivity temperature sensor based on a small air core (10 μm) hollow core fiber (SACHCF) structure is proposed. Co-excitation of both anti-resonant reflecting optical waveguide (ARROW) and Mach-Zehnder interferometer (MZI) guiding mechanisms in transmission are demonstrated. It is found that the strain sensitivity of the proposed SACHCF structure is decreased over one order of magnitude when a double phase condition (destructive condition of MZI and resonant condition of ARROW) is satisfied. In addition, due to its compact size and a symmetrical configuration, the SACHCF structure shows ultra-low sensitivity to curvature and twist. Experimentally, a high temperature sensitivity of 31.6 pm/°C, an ultra-low strain sensitivity of −0.01pm/με, a curvature sensitivity of 18.25 pm/m−1, and a twist sensitivity of −22.55 pm/(rad/m) were demonstrated. The corresponding temperature cross sensitivities to strain, curvature and twist are calculated to be −0.00032 °C/με, 0.58 °C/m−1 and 0.71 °C/(rad/m), respectively. The above cross sensitivities are one to two orders of magnitude lower than that of previously reported optical fiber temperature sensors. The proposed sensor shows a great potential to be used as a temperature sensor in practical applications where influence of multiple environmental parameters cannot be eliminated.