The nuclear spin-spin coupling constant td(laC, H) in t3C-enriched methane gas has been observed by laC resonance to increase from 125.264Hz at 180K to 125.347Hz at 369 K. The dependence on temperature is non-linear with a much steeper variation at higher temperatures. Very similar results are observed in 1H resonance. There appears to be a very slight dependence of 1j(13C, H) on density at the lower temperatures. The theory of the temperature dependences of 1J(tac, H) and 1J(t3C, D) in the low density, gaseous, isotopomers of methane ~aCHxD,_x is presented in terms of the coefficients of a single carbon-13 proton spin-spin coupling surface, the elements of the L tensor of vibration-rotation theory and the average values of reduced normal coordinates and their squares. Results are applicable to the temperature dependences of all X, Y coupling constants and Y nuclear shielding constants in X Y, molecules of T~ symmetry. Application of the theory to the results on taCH, gives an equilibrium value of 119.18(16)Hz which shows that the nuclear motion contributes more than 6 Hz to the observed coupling. The quantity (J, + 3Js) is found to be 368(10)HzA-1; Jr is the derivative of the coupling with respect to the length of the bond involved in the coupling and Js is the derivative with respect to the length of a bond not involved in the coupling.