  We use FUSE and STIS spectra to study intergalactic absorption towards the
quasar PG1259+593 (z=0.478). We identify 135 intergalactic absorption lines
with equivalent widths >10mA, tracing 78 absorption components in 72 Ly
alpha/beta absorption-line systems. We concentrate on the distribution and
physical properties of the WHIM as sampled by OVI and intrinsically broad Ly
alpha lines. The number of intervening OVI absorbers for equivalent widths W>24
mA is 3-6 over an unobscured redshift path of dz=0.368. This implies a number
density of OVI systems, dN/dz, of ~8-16 along this sight line. This range is
consistent with estimates from other sight lines, supporting the idea that
intervening intergalactic OVI absorbers contain an substantial fraction of the
baryonic mass in the low-redshift Universe. We identify a number of broad Ly
alpha absorbers with large Doppler parameters (b~40-200 km/s) and low column
densities (N(HI)<10^14 cm^-2). For pure thermal broadening, these widths
correspond to temperatures of ~1x10^5 to 3x10^6 K. While these broad absorbers
could be caused by blends of multiple, unresolved lines, continuum undulations,
or by kinematic flows and Hubble broadening, we consider the possibility that
some of these features are single-component, thermally broadened Ly alpha
lines. These systems could represent WHIM absorbers that are too weak, too
metal-poor, and/or too hot to be detected in OVI. If so, their widths and their
frequency in the PG1259+593 spectrum imply that these absorbers trace an even
larger fraction of the baryons in the low-redshift Universe than the OVI
absorbing systems (abridged version).
