present a detailed study of the HI 21 cm absorption system at z = 0.0912 to
ward the radio quasar B0738+313. The uncommonly narrow main absorption line
and weak secondary line are resolved for the first time and have FWHM velo
cities of Delta v(1) = 3.7 and Delta v(2) = 2.2 km s(-1) (main and secondar
y components, respectively). In addition, we find it necessary to add a thi
rd, broader shallow component to obtain a good fit to the spectrum. Althoug
h the harmonic mean spin temperature calculated by comparison of the 21 cm
lines to the damped Ly alpha line is [T-s] = 775 +/- 100 K, the thermal kin
etic temperatures of the two narrow components, calculated from their width
s, are much lower: T-k less than or equal to 297 +/- 3 and less than or equ
al to 103 +/- 10 K, respectively. This is the first case of a redshifted ab
sorption system for which T-k is measured to be less than [T-s]. We discuss
this result in the context of a two-phase gas model, in which the damped L
y alpha gas is sensitive to a significant neutral column density of warm-ph
ase gas as well as the cold-phase gas of the narrow 21 cm lines. The third
component is interpreted as representing the warm-phase gas with T-k less t
han or equal to 5050 +/- 950 K. The combined column density of the three 21
cm components is approximately equal to that derived from fits to the damp
ed Ly alpha line.