  We present a study of the Ly\alpha forest at z<0.4 from which we conclude
that at least 20% of the total baryons in the universe are located in the
highly-ionized gas traced by broad Ly\alpha absorbers. The cool photoionized
low-z intergalactic medium (IGM) probed by narrow Ly\alpha absorbers contains
about 30% of the baryons. We further find that the ratio of broad to narrow
Ly\alpha absorbers is higher at z<0.4 than at 1.5<z<3.6, implying that a larger
fraction of the low redshift universe is hotter and/or more kinematically
disturbed. We base these conclusions on an analysis of 7 QSOs observed with
both FUSE and the HST/STIS E140M ultraviolet echelle spectrograph. Our sample
has 341 HI absorbers with a total unblocked redshift path of 2.064. The
observed absorber population is complete for log N_HI>13.2, with a column
density distribution f(N_HI) \propto N^-\beta_HI. For narrow (b<40 km/s)
absorbers \beta = 1.76+/-0.06. The distribution of the Doppler parameter b at
low redshift implies two populations: narrow (b<40 km/s) and broad (b>40 km/s)
Ly\alpha absorbers (referred to as NLAs and BLAs, respectively). Both the NLAs
and some BLAs probe the cool (T~10^4 K) photoionized IGM. The BLAs also probe
the highly-ionized gas of the warm-hot IGM (T~10^5-10^6 K). The distribution of
b has a more prominent high velocity tail at z<0.4 than at 1.5<z<3.6, which
results in median and mean b-values that are 15-30% higher at low z than at
high z. The ratio of the number density of BLAs to NLAs at z<0.4 is a factor of
\~3 higher than at 1.5<z<3.6.
