Calibrating the HISA temperature: Measuring the temperature of the Riegel-Crutcher cloud

H I self-absorption (HISA) clouds are clumps of cold neutral hydrogen (H I) visible in front of warm background gas, which makes them ideal places to study the properties of the cold atomic component of the interstellar medium. The Riegel-Crutcher (R-C) cloud is the most striking HISA feature in the Galaxy. It is one of the closest HISA clouds to us and is located in the direction of the Galactic Centre, which provides a bright background. High-resolution interferometric measurements have revealed the filamentary structure of this cloud; however, it is difficult to accurately determine the temperature and the density of the gas without optical depth measurements. In this paper, we present new H I absorption observations with the Australia Telescope Compact Array against 46 continuum sources behind the R-C cloud to directly measure the optical depth of the cloud. We decompose the complex H I absorption spectra into Gaussian components using an automated machine learning algorithm. We find 300 Gaussian components, from which 67 are associated with the R-C cloud (0 < v_LSR < 10 km s^-1,  full width at half maximum < 10 km s^-1). Combining the new H I absorption data with H I emission data from previous surveys, we calculate the spin temperature and find it to be between 20 and 80 K. Our measurements uncover a temperature gradient across the cloud with spin temperatures decreasing towards positive Galactic latitudes. We also find three new OH absorption lines associated with the cloud, which support the presence of molecular gas.