Thermally-broadened Lya absorbers (BLAs) offer an alternate method to using highly-ionized metal absorbers (OVI, OVII, etc.) to probe the warm-hot intergalactic medium (WHIM, T=10^5-10^7 K). Until now, WHIM surveys via BLAs have been no less ambiguous than those via far-UV and X-ray metal-ion probes. Detecting these weak, broad features requires background sources with a well-characterized far-UV continuum and data of very high quality. However, a recent HST/COS observation of the z=0.03 blazar Mrk421 allows us to perform a metal-independent search for WHIM gas with unprecedented precision. The data have high signal-to-noise (S/N~50 per ~20 km/s resolution element) and the smooth, power-law blazar spectrum allows a fully-parametric continuum model. We analyze the Mrk421 sight line for BLA absorbers, particularly for counterparts to the proposed OVII WHIM systems reported by Nicastro et al. (2005a,b) based on Chandra/LETG observations. We derive the Lya profiles predicted by the X-ray observations. The signal-to-noise ratio of the COS data is high (S/N~25 per pixel), but much higher S/N can be obtained by binning the data to widths characteristic of the expected BLA profiles. With this technique, we are sensitive to WHIM gas over a large (N_H, T) parameter range in the Mrk421 sight line. We rule out the claimed Nicastro et al. OVII detections at their nominal temperatures (T~1-2x10^6 K) and metallicities (Z=0.1 Z_sun) at >2 sigma level. However, WHIM gas at higher temperatures and/or higher metallicities is consistent with our COS non-detections.
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