The development of photonic quantum information technologies requires research on the properties of optical adhesives at cryogenic temperatures. In the process of developing microfiber (MF)-coupled superconducting nanowire single-photon detectors (SNSPDs), we invented a cryogenic-temperature refractive index (RI) measurement method based on a kind of MF device. The device was put into the cryostat to observe the variance of MF transmittance with temperature. Then an RI-temperature relationship was established through the correspondence between the confinement conditions of MFs of various diameters in an optical adhesive-${{\rm MgF}_2}$MgF2 environment and transmittance-temperature curves. Using this method, we analyzed the thermal-optical properties of a commercial fluorinated acrylic optical adhesive and obtained the RI values of the adhesive at various temperatures. The results were successfully applied in the development of broadband and high-efficiency MF-coupled SNSPDs.