Read here and here. It is well established climate models are unable to accurately predict the dirunal temperature range. This failure is directly related to climate models' lousy ability at predicting daily minimum temperatures; in addition, a significant portion of the modern global warming record used as inputs to IPCC climate models, is due to higher nighttime temperatures (minimum). (click on image to enlarge; image source)
This prediction failure has been due to the climate models assuming that minimum temperatures (nighttime temps) are driven by atmospheric CO2 levels, resulting in predicted minimum temperatures that are too high. According to McNider et al., the minimum temperatures are more a fucntion of heat redistribution during evening hours versus additional nighttime heat being added by greenhouse gases. Compounding this problem, climate models cannot simulate the heat redistribution physics affecting nighttime temperatures.
The authors conclude that minimum temperatures should no longer be used as a proxy for global atmospheric warming. This implies that it is likely global warming attributed to CO2 levels has been signficantly overstated.
"One of the most significant signals in the thermometer-observed temperature record since 1900 is the decrease in the diurnal temperature range over land, largely due to warming of the minimum temperatures...Climate models have in general not replicated the change in diurnal temperature range well. Here we would like to try to distinguish between warming in the nocturnal boundary layer due to a redistribution of heat and warming due to the accumulation of heat...It is likely that the observed warming in minimum temperature, whether caused by additional greenhouse forcing or land use changes or other land surface dynamics, is reflecting a redistribution of heat by turbulence-not an accumulation of heat. Because minimum temperatures in the stable boundary layer are not very robust measures of the heat content in the deep atmosphere and climate models do not predict minimum temperatures well, minimum temperatures should not be used as a surrogate for measures of deep atmosphere global warming.” [R.T. McNider, J.R. Christy and A. Biazar 2011: Earth and Environmental Science]