What is happening to global temperatures in reality? The answer is: almost nothing for more than 10 years.
The lack of any statistically significant warming for over a decade has made it more difficult for the United Nations Intergovernmental Panel on Climate Change (IPCC) and its supporters to demonize the atmospheric gas CO2 which is released when fossil fuels are burned.
CO2 is not a pollutant. Life on earth flourished for hundreds of millions of years at much higher CO2 levels than we see today. Increasing CO2 levels will be a net benefit because cultivated plants grow better and are more resistant to drought at higher CO2 levels, and because warming and other supposedly harmful effects of CO2 have been greatly exaggerated. Nations with affordable energy from fossil fuels are more prosperous and healthy than those without.
The direct warming due to doubling CO2 levels in the atmosphere can be calculated to cause a warming of about one degree Celsius. The IPCC computer models predict a much larger warming, three degrees Celsius or even more, because they assume changes in water vapor or clouds that supposedly amplify the direct warming from CO2. Many lines of observational evidence suggest that this "positive feedback" also has been greatly exaggerated.
There has indeed been some warming, perhaps about 0.8 degrees Celsius, since the end of the so-called Little Ice Age in the early 1800s. Some of that warming has probably come from increased amounts of CO2, but the timing of the warming—much of it before CO2 levels had increased appreciably—suggests that a substantial fraction of the warming is from natural causes that have nothing to do with mankind.
It is easy to be confused about climate, because we are constantly being warned about the horrible things that will happen or are already happening as a result of mankind's use of fossil fuels. But these ominous predictions are based on computer models. It is important to distinguish between what the climate is actually doing and what computer models predict. The observed response of the climate to more CO2 is not in good agreement with model predictions.
The most important component of climate science is careful, long-term observations of climate-related phenomena, from space, from land, and in the oceans. If observations do not support code predictions—like more extreme weather, or rapidly rising global temperatures—Feynman has told us what conclusions to draw about the theory - it is wrong.