Shareholders are calling on British Petroleum to "stress-test" its business to make sure it's complying with government commitments not to let global temperatures rise more than 2C.
If there's a rise any higher than that, "dangerous" climate change is expected.
The Church and other investors have already asked the same of rival Shell.
It's also calling on the two companies to commit to reducing emissions and investing in renewable energy.
BP includes the pension funds for both the Church of England and the Methodist Church.
The 'resolution' added to by the Church will be viewed at by shareholders at BP and Shell's annual general meetings in April and May.