Abstract: Since 1850 the global surface temperature has warmed by about 0.9 oC. The CMIP5 computer climate models adopted by the IPCC have projected that the global surface temperature could rise by 2-5 oC from 2000 to 2100 for anthropogenic reasons. These projections are currently used to justify expensive mitigation policies to reduce the emission of anthropogenic greenhouse gases such as CO2. However, recent scientific research has pointed out that the IPCC climate models fail to properly reconstruct the natural variability of the climate. Indeed, advanced techniques of analysis have revealed that the natural variability of the climate is made of several oscillations spanning from the decadal to the millennial scales (e.g. with periods of about 9.1, 10.4, 20, 60, 115, 1000 years and others). These oscillations likely have an astronomical origin. The same considerations yield to the conclusion that the IPCC climate models severely overestimate the anthropogenic climatic warming by about two times. Herein I demonstrate a number of failures of the IPCC models and I propose a semi-empirical climate model able to reconstruct the natural climatic variability since Medieval times. I show that this model projects a very moderate warming until 2040 and a warming less than 2 oC from 2000 to 2100 using the same anthropogenic emission scenarios used by the CMIP5 models. This result suggests that climatic adaptation policies, which are less expensive than the mitigation ones, could be sufficient to address most of the consequences of a climatic change during the 21st century. Finally, I show that a temperature forecast made in 2011 by Scafetta (Ref. 25) based on harmonic oscillations has well agreed with the global surface temperature data up to August 2016.