What a simplistic, uneducated perspective! Life obviously adapts to warmer or colder climates, but over long stretches of time, meaningless to present-day human society or existence--hundreds of thousands, or millions of years.
But when climate changes too rapidly--on the scale of years or decades as it is today, as opposed to millennia in the past, plant life cannot adapt, and vast numbers of plants and the animals that depend on them will perish. Fungi and bacteria, which thrive on carrion and evolve far more quickly, will be fine, however. It will take a vastly long time for anything resembling a healthy ecosystem to evolve in the new, parched climate conditions we have kick-started in our short-sighted greed and ignorance.