Evolution is adapting we adapted to climate before, or otherwise how are we alive now? We adapted to technology, did we not? I think one day we will be able to use technology to help is adapt to climate change. Technology already helped us evolve because now we know what the weather in the future is going to be.
The world has been periodically warmer and colder for years. Life managed to live on in a world with regular below freezing temperatures, think ice ages, and studies show the dinosaurs lived in a much warmer and more humid climate (thus all the vegetation from that time). Will the same animals exist? Probably not, but that is the point of evolution.
Yes, I think that evolution does and will continue have to more evidence of occurring that climate change ever will. Evolution is taught in high schools, and climate change is just a theory that only a few minority scientists really believe in. I think that evolution can be more proven than climate change.
Evolution can not beat climate change. Evolution is when animals or people evolve to fit to the climate or area that they are placed in. However, to evolve or better fit themselves into that climate the weather and surroundings of that place have to change first. Otherwise are bodies have no way of knowing they need to adapt.
The environmental pressure surrounding the current global climate change is too rapid for most "higher" animals to keep up. Mutation rates occur only so fast in a population, which determines how well that population can adapt to a changing environment.
However, humans are technologically capable- we are not at the mercy of our environment as most species are. Smaller animals, birds, insects, fish, and microbes are also unlikely to be as affected as larger species.