The role of banks in supporting the low-carbon transition has proved controversial as banks have maintained investment in polluting industries. But has there been a good case for them to do otherwise? The central explanation given for banks reallocating their portfolio and imposing a carbon premium on polluting firms is that of climate transition risk. To explicit this channel I build a simple model for lending decisions, based on three pillars: a mathematical formalization of the concept of climate sentiments, the policy-dependent net present value of firms' capital, and the Merton model. First, I examine what maximum changes in the credit market would be expected from the so-called risk channel of green finance. Second, I consider discrepancies in climate sentiments between lenders and borrowers, to determine when banks could push borrowers to green their operations, or prevent them from doing so. The findings suggest that, even with banks having strong beliefs in the implementation of climate policies, the ensuing changes in the price of debt are limited relative to macro-level variations and thus may not be enough of a decarbonization incentive alone. Macro-prudential measures that complement carbon pricing and policies that limit the lending volume would then be necessary to green the economy more through the financial system.