We use the millennium Arecibo 21 cm absorption-line survey measurements to examine the issue of the non-thermal contribution to the observed Galactic H i line widths .
If we assume a simple , constant pressure model for the H i in the Galaxy , we find that the non-thermal contribution to the line width , v _ { nt } scales as v ^ { 2 } _ { nt } \propto l ^ { \alpha } , for v _ { nt } larger than \sim 0.7 km s ^ { -1 } .
Here l is a derived length scale and \alpha \sim 0.7 \pm 0.1 .
This is consistent with what one would expect from a turbulent medium with a Kolmogorov scaling .
Such a scaling is also predicted by theoretical models and numerical simulations of turbulence in a magnetized medium .
For non-thermal line widths narrower than \sim 0.7 km s ^ { -1 } , this scaling breaks down , and we find that the likely reason is ambiguities arising from Gaussian decomposition of intrinsically narrow , blended lines .
We use the above estimate of the non-thermal contribution to the line width to determine corrected H i kinetic temperature .
The new limits that we obtain imply that a significantly smaller ( \sim 40 \% as opposed to 60 % ) fraction of the atomic interstellar medium in our Galaxy is in the warm neutral medium phase .