We present a detailed study of the H i 21cm absorption system at z = 0.0912 towards the radio quasar B0738+313 .
The uncommonly narrow main absorption line and weak secondary line are resolved for the first time and have FWHM velocities of \Delta v _ { 1 } = 3.7 and \Delta v _ { 2 } = 2.2 km s ^ { -1 } ( main and secondary component respectively ) .
In addition we find it necessary to add a third , broader shallow component to obtain a good fit to the spectrum .
Although the harmonic mean spin temperature calculated by comparison of the 21cm lines to the damped Ly \alpha line is < T _ { \mathrm { s } } > = 775 \pm 100 K , the thermal kinetic temperatures of the two narrow components , calculated from their widths , are much lower : T _ { \mathrm { k } } \leq 297 \pm 3 and \leq 103 \pm 10 K respectively .
This is the first case of a redshifted absorption system for which T _ { \mathrm { k } } is measured to be less than < T _ { \mathrm { s } } > .
We discuss this result in the context of a two phase gas model , in which the damped Ly \alpha gas is sensitive to a significant neutral column density of warm phase gas as well as the cold phase gas of the narrow 21cm lines .
The third component is interpreted as representing the warm phase gas with with T _ { \mathrm { k } } \leq 5050 \pm 950 K. The combined column density of the three 21cm components is approximately equal to that derived from fits to the damped Ly \alpha line .