In The Forgiving Air , Richard Somerville, who is director of climate research at Scripps Institution of Oceanography, describes the considerations that go into scientific weather and climate prediction in a way that is accessible to anyone interested in the subject in a general way, from the high school level up. The book is a good read, and there is no mathematics in it other than the powers of ten. The greenhouse effect, the ozone hole, acid rain, reflectivity of ice caps are emphasized.
More carbon dioxide leads to more atmospheric water vapor, which leads to higher temperatures.
On average, they cool. Somerville bases his assessments of meteorological trends on a variety of mathematical models, but he recognizes the need for skepticism and improvements. The dire predictions of the effects of the fierce oil well fires ignited in Kuwait during the gulf war turned out to be over-pessimistic. Microweather, e.g., a hurricane or a tornado, has its own difficulties. Chaos theory informs us that there appear to be absolute limits to what mathematics can accomplish with the best of models and the fastest machines.