But I don't understand, like I said above, how capitalism is causing it and how not-capitalism would solve it.

But I don’t see that any capitalism alternative has a good answer either, so still I don’t see how capitalism is the “bad guy”.

A couple notes on this. Firstly, just as an argument perspective, this is a burden of proof fallacy. Just because "not-capitalism" may not have a good answer, doesn't mean capitalism has a good one or even just a better one. I could be mischaracterising your argument, if so my bad, this is just how it reads to me. Secondly, I personally believe that socialism offers a better answer and a good one at that, which all revolves around incentives. A collective-ownership structure has more incentive for social well being, such as avoiding climate disaster, than a purely capitalist structure does.

As a side-note, I also think you're mischaracterising capitalism by including governing bodies, but you're doing it in a manner that's only one logical step away from socialism. By a government placing restrictions on a market or producer, say by defining a carbon emission cap, the market is no longer operating at true efficiency. While not fully capitalist anymore, that's still okay though as it's serving a social purpose. Zoom out a little and you can see other markets in which the government should set limits in. Now the whole economy isn't operating as a true free market. In this case, the government is defining what the social good is, and (at least in democratic nations), the government defines that based on the voice of the people. The problem with this is that it's reactive. I can pass as many laws as I want saying you can't emit carbon above a certain level, but I can only enforce it after you've gone over that cap at which point the damage is done, and some may make the economic calculation that it's worth it if you get more profits (fines are in essence "legal for a price" after all). If the government owns the industry, this can be prevented before happening.

Also free markets can exist without capitalism. I think another person somewhere on this thread mentioned worker co-ops, which are not a capitalist institution.

As a parting thought, I would also point out that one of if not the most efficient energy companies in the United States (in terms of energy produced per dollar input) is the TVA, a state-owned enterprise.