The empirical line parameters of 12268 transitions of methane at 80 K have been constructed for the 1.58 µm transparency window (6165-6750 cm-1). This line list, WKC, which is of particular interest for several planetary applications, was obtained from high sensitivity spectra recorded by CW-Cavity Ring Down Spectroscopy at low temperature. By comparison with a spectrum of CH3D recorded separately by Fourier Transform Spectroscopy at low temperature (90-120 K), most of the transitions of monodeuterated methane, CH3D, in "natural" abundance in the sample were identified. The CH3D relative contribution in the considered region is observed to be much larger at 80 K than at room temperature. In particular, CH3D is found strongly dominant in a narrow spectral window near 6300 cm-1 corresponding to the highest transparency region. Using a similar line list constructed at room temperature (A. Campargue, L. Wang, A. W. Liu, S. M. Hu and S. Kassi, Chem. Phys., 373 (2010) 203-210), the low energy values of the transitions observed both at 80 K and at room temperature were derived from the variation of their line intensities. The good quality of the obtained empirical low energy values is demonstrated by the marked propensity of the empirical low J values of the CH4 transitions to be close to integers. The WKC line lists at 80 K and room temperature provided as Supplementary Material allow one accounting for the temperature dependence of methane absorption between these two temperatures. The importance of the 80 K line list for the study of Titan and other methane containing planetary atmospheres is underlined and further improvements are proposed.