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We discuss physical properties and baryonic content of broad Lyα absorbers (BLAs) at low redshift. These absorption systems, recently discovered in high-resolution, high-signal to noise quasar absorption line spectra, possibly trace the warm-hot intergalactic medium (WHIM) in the temperature range between 10⁵ and 10⁶K. The central idea is that in ionization equilibrium WHIM filaments should contain a very small fraction of neutral gas (f_HI∼10^–5-10^–6, typically), giving rise to weak intervening HI Lyα absorption. Due to the high temperature of the WHIM, these Lyα absorbers must be thermally broadened to Doppler parameters (b values) ≥40km/s. It is expected, however, that also non-thermal line broadening processes, line blends, and noise features can mimic broad spectral features, complicating the quantitative estimate of the baryon content of the BLAs. To extend previous BLA measurements we have reanalyzed archival STIS data of the two quasars H1821+643 and PG0953+415 and have identified 13 BLA candidates along a total (unblocked) redshift path of Δ z=0.440. Combining our measurements with previous results for the lines of sight toward PG1259+593 and PG1116+215, the resulting new BLA sample consists of 20 reliably detected systems as well as 29 additional tentative cases, implying a BLA number density of dN_BLA/dz=22-53. Eight BLAs show associated absorption from HI Lyβ and/or OVI. The comparison between Lyα, Lyβ, and Ovi line widths suggests that non-thermal broadening and noise features substantially affect the observed BLA b value distribution. However, it remains unclear whether BLAs and Ovi absorbers trace the same gas phase in the WHIM filaments. We estimate that the contribution of BLAs to the baryon density at z=0 is Ω_b(BLA)≥0.0027h₇₀^–1 for absorbers with log [N(cm^–2)/b(km/s)]>11.3. This number indicates that WHIM broad Lyα absorbers contain a substantial fraction of the baryons in the local Universe.