Climate risks are now fully recognized as financial risks by asset managers, investors, central banks, and financial supervisors. As a result, the integration of climate risk metrics into risk management processes is moving up agendas worldwide. In that context, a rapidly growing number of market participants and financial authorities are exploring which metrics to use to capture climate risks, and to what extent the use of different metrics delivers heterogeneous results. This discussion note takes a first step in analyzing the convergence in assessments of climate-related transition risks across metrics providers, based on the ECB corporate bond portfolio. Our findings show that firms’ risk assessments across metrics are fairly heterogeneous but tend to converge on which firms are most and least exposed to transition risks. We also show that the temperature targets and time horizons underlying the metrics matter, although moderately, for the assessment of firms’ risk exposure and that providers using similar methodologies tend to deliver more convergent assessments. Our findings contribute to the growing recognition that asset managers, investors, central banks and financial supervisors can and should use available metrics to better integrate climate risks into risk management and financial supervision.