Recent Chandra and XMM X-ray observations of rich clusters of galaxies have shown that the amount of hot gas which is cooling below ~1 keV is generally more modest than previous estimates. Yet, the real level of the cooling flows, if any, remains to be clarified by making observations sensitive to different temperature ranges. As a follow-up of the FUSE observations reporting a positive detection of the OVI doublet at 1032, 1038 Angstrom in the cluster of galaxies Abell 2597, which provided the first direct evidence for ~3x10^5 K gas in a cluster of galaxies, we have carried out sensitive spectroscopy of two rich clusters, Abell 2029 and Abell 3112 (z~0.07) located behind low HI columns. In neither of these clusters could we detect the OVI doublet, yielding fairly stringent limits of ~27 Msun yr-1 (Abell 2029) and ~25 Msun yr-1 (Abell 3112) to the cooling flow rates using the 10^5-10^6 K gas as a tracer. The non-detections support the emerging picture that the cooling-flow rates are much more modest than deduced from earlier X-ray observations.
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