This study examines how ambiguity in news media attention to climate change, capturing variability in how climate-related events are covered across media outlets, affects corporate bond pricing and intertemporal hedging demand. We show that investors prefer bonds with strong potential to hedge against climate risk, thereby accepting lower future returns. This hedging premium is significantly attenuated when media ambiguity is high: during periods of elevated ambiguity, the standard hedging incentive weakens and, for physical climate risks, reverses entirely. Long-term bonds are more sensitive to physical climate risk hedging demand, while transition risk hedging is more pronounced for short-term bonds. When both transition risk and ambiguity are elevated, investors favor bonds issued by firms with low climate exposure, whose reputational resilience preserves their hedging value under uncertain conditions.