Thermally broadened Ly \alpha absorbers ( BLAs ) offer an alternative method to highly-ionized metal lines for tracing the warm-hot intergalactic medium ( WHIM ) at T > 10 ^ { 5 } K. However , observing BLAs requires data of high quality and accurate continuum definition to detect the low-contrast features , and a good knowledge of the velocity structure to differentiate multiple blended components from a single broad line . Even for well-characterized absorption profiles , disentangling the thermal line width from the various thermal and non-thermal contributors to the observed line width is ambiguous . We compile a catalog of reliable BLA candidates along seven AGN sight lines from a larger set of Ly \alpha absorbers observed by the Space Telescope Imaging Spectrograph ( STIS ) on the Hubble Space Telescope ( HST ) . We compare our measurements based on independent reduction and analysis of the data to those published by other research groups . We examine the detailed structure of each absorber and determine a reliable line width and column density . Purported BLAs are grouped into probable ( 15 ) , possible ( 48 ) and non-BLA ( 56 ) categories . Combining the first two categories , we infer a line frequency ( d { \cal N } / dz ) _ { BLA } = 18 \pm 11 , comparable to observed O vi absorbers , also thought to trace the WHIM . We discuss the overlap between BLA and O vi absorbers ( 20-40 % ) and the distribution of BLAs in relation to nearby galaxies ( O vi detections in BLAs are found clouser to galaxies than O vi non-detections ) . We assume that the line width determined through a multi-line curve-of-growth ( COG ) is a close approximation to the thermal line width . Based on 164 measured COG H i line measurements , we statistically correct the observed line widths via a Monte-Carlo simulation . Gas temperature and neutral fraction f _ { HI } are inferred from these statistically-corrected line widths and lead to a distribution of total hydrogen columns . Summing the total column density over the total observed pathlength , we find a BLA contribution to the closure density of \Omega _ { BLA } = 6.3 ^ { +1.1 } _ { -0.8 } \times 10 ^ { -3 } h _ { 70 } ^ { -1 } based on 10 ^ { 4 } Monte-Carlo simulations of each BLA system . There are a number of critical systematic assumptions implicit in this calculation , and we discuss how each affects our results and those of previously published work . In particular , the most comparable previous study by Lehner et al . ( 21 ) gave \Omega _ { BLA } = 3.6 \times 10 ^ { -3 } h _ { 70 } ^ { -1 } or 9.1 \times 10 ^ { -3 } h _ { 70 } ^ { -1 } , depending on which assumptions were made about hydrogen neutral fraction . Taking our value , current O vi and BLA surveys can account for \sim 20 % of the baryons in the local universe while an additional \sim 29 % can be accounted for in the photoionized Ly \alpha forest ; about half of all baryons in the low- z universe are found in the IGM . Finally , we present new , high-S/N observations of several of the BLA candidate lines from Early Release Observations made by the Cosmic Origins Spectrograph on HST .