The high resolution absorption spectra of 13CH4 were recorded at 81 K by differential absorption spectroscopy using a cryogenic cell and a series of Distributed Feed Back (DFB) diode lasers and at room temperature by Fourier transform spectroscopy. The investigated spectral region corresponds to the high energy part of the 13CH4 tetradecad dominated by the 23 overtone near 5988 cm-1. Empirical line lists were constructed containing, respectively, 1629 13CH4 transitions detected at 81 K (5852-6124 cm-1) and 3481 features (including 85 lines of 12CH4) measured at room temperature (5850-6150 cm-1); the smallest measured intensities are about 3×10-26 and 4×10-25 cm/molecule at 81 K and 296 K, respectively. The lower state energy values were derived for 1196 13CH4 transitions from the variation of the line intensities between 81 K and 296 K. These transitions represent 99.2% and 84.6 % of the total absorbance in the region, at 81 K and 296 K respectively. Over four hundred additional weak features were measured at 81 K and could not be matched to lines observed at room temperature. The quality of the resulting empirical low energy values is demonstrated by the excellent agreement with the already-assigned transitions and the clear propensity of the empirical low J values to be close to integers. The two line lists at 81 K and at 296 K provided as Supplementary Material will enable future theoretical analyses of the upper 13CH4 tetradecad.