Jerome Powell
Officially, Congress sets the Fed's priorities but the Fed has independence on how to carry out its mandates. Unofficially, the Fed just adopted its own new mandate.

The Evolution of an Idea

The Federal Reserve Bank of Richmond explains the Evolution of an Idea.
Since 1977, the Federal Reserve has operated under a mandate from Congress to "promote effectively the goals of maximum employment, stable prices, and moderate long term interest rates" — what is now commonly referred to as the Fed's "dual mandate." The idea that the Fed should pursue multiple goals can be traced back to at least the 1940s, however, with shifting emphasis on which objective should be paramount.
That snip is from 2011 and matches what the Fed has said over the years.

I do not believe I see the words "climate change" anywhere in the "dual mandate".

Fed Joins Climate Change Network

Despite climate change being no part of the Fed's mandate the Fed Joins Climate Network, to Applause From the Left.
The Fed's board in Washington voted unanimously to become a member of the Network of Central Banks and Supervisors for Greening the Financial System.

"The public will expect that we do figure out what are the implications of climate change for financial stability, and that we do put policies in place," Jerome H. Powell, the Fed chair, said this month at a Senate hearing. "The broad response to climate change on the part of society really needs to be set by elected representatives — that's you. We see implications of climate change for the job that you've given us, and that's what we're working on."
Greening of the Fed

"We see implications of climate change for the job that you've given us, and that's what we're working on," said Powell.

Excuse me for asking but when did Congress add climate change to the Fed's list of mandates?

Given the Fed has blown three economic bubbles in succession, has never spotted a recession in advance, and is totally clueless about price stability, perhaps it ought to stick to monetary policy.

Then again, if the Fed were to abandon monetary policy and just let the free market work, that could be an adequate tradeoff for letting the Fed pontificate on climate change.