The planet's climate has undergone change for most of it's history. Those changes occur for a variety of reasons such as volcanism, astronomical impact, plate tectonics, changes in ocean currents and the Earth's orbit to name but a few. Those changes are a natural progression and they have been one of the engines powering evolutionary change and life itself. No matter how severe climate changes have been in the past, life and the planet have always survived.
All we are seeing now is yet another climate change. This one may have been affected by humans but it is nowhere near as severe as other changes the Earth has seen. Many species will fail to cope and become extinct but that opens the door for other species to evolve and fill the vacant niches. Although humans are in the process of destroying themselves by unchecked population growth, life on Earth will continue and the planet survive. In 5 million years time the failed human species will be a distant and forgotten nightmare but life and planet Earth will have rebounded to be as healthy as they were a million years ago.