It wasn't only Carter who thought we had hit or were close to hitting peak oil production. There were members of both parties who thought it likely. Also, you cite this as an example of him being wrong about an environmental issue, but that was more of an economic issue. I'm surprised you didn't cite his opposition to nuclear power as an example of where he was wrong on an environmental issue - yes, in hindsight we now know that wasn't the way to go, but we have to remember that in the 70s anti-nuke
was the environmental position, while they were starting to know about climate change, they didn't yet have the idea that nuclear power (which was becoming increasingly unpopular) would be a good way of avoiding that.
The other thing to remember is that Carter was warning that being dependent on foreign oil was bad for US national security. This was why he was doing what he could to get us to reduce our energy consumption. As for the thermostats, I don't recall that we were being mandated to turn down the thermostats in our houses and I was there.
As for the inflation, he inherited a lot of that from the wartime spending expansion of his predecessors - Arab oil embargoes didn't help. And he did name Paul Volcker to lead the Fed even though in his interview Volcker told him that the only remedy would be to drastically raise interest rates. Volcker thought that he definitely wouldn't get the job (it was the year before an election year) so he was surprised when Carter picked him. So in that sense, Carter played a key role in killing the 70s inflation (which had been a problem even prior to Carter being elected - Remember Ford's WIN - Whip Inflation Now - buttons?) In the end, Volcker did what he said he was going to do. 10 year treasury rates hit ~15%. The economy swooned and it was a big factor in Carter not winning re-election, but that ended up killing the 70s inflation. He had the guts to pick Volcker even though it would not be good for him politically, but he knew that it would be the best choice for the economy in the longrun.
Also in regards to inflation, it should be remembered that Carter was a fiscal conservative trying to reign in spending, but his own party faught him on this. It's why Ted Kennedy primaried him in the 1980 Democratic primaries: he considered Carter to be too much of a tightwad.