I don't see humans going extinct; we can find ways to adapt. Scientists are already growing meat in labs. Vegetables can be grown indoors. So we can find new ways to feed ourselves — especially with the help of AI.
Soylent Green may become a reality someday. Why bother burying dead bodies when we can use them as food? Maybe not for humans, but to feed other animals. Or to feed poor people.
Eventually, we'll get 100% of our power from clean, renewable sources. That could happen by the end of the 21st century. It may take another hundred years for our climate to return to normal, but in the meantime, humans are not going extinct. Granted, some people (people without money) will have it a little rough.
No matter how hot or cold it gets, with advances in heating and air conditioning technologies, we can maintain suitable living conditions. We might have to refrain from going outside except in emergencies or to construct new buildings, but for the most part, we could exist indoors without too much discomfort. We'd just have to take vitamin D to compensate for lack of exposure to sun rays.