It seems to me that when we talk about capitalism, we have different notions in mind. So, as briefly as I can, I will try to answer your question

How could possibly think Capitalism is the cause of global warming?

Capitalism and it's industrialization, have been going on for over two centuries. It's easy to find the metrics that prove that CO2 emissions have increased with industrialization.

As an economic system, it deals with exploitation of humans, exploitation of nature, with the help of some tech for profit, and this profit needs to be reinvested into making more profit, non-stop. Infinite growth is embedded in the model, even tho our planet has limits. And regulatory frameworks, obviously don't work. Otherwise we would be having a different conversation.

In more recent decades, capitalist globalization took over the world. The countries that were previously colonized, instead of gaining their real independence, they got trapped in an economical colonization (neocolonialism) and westerners kept exploiting these places. Famous example of mining companies exploitation come mostly from Canada, Australia and US. China came late to the game and currently is in 4th position [link].

For you, what is the reason of the climate crisis?