RIND: Our GCM looked at diurnal temperature change for doubled CO2 . We found that for a 4° warming we got about a 10 percent change, or 1°C. That was primarily during the summer, so we did not get the one-to-one correspondence you see in the data. I also wanted to mention that the ISCCP data set can't get optical thicknesses for nighttime clouds, since they can't measure the albedos.
KARL: I should perhaps add that while most of the CO2-doubling models show a decrease in diurnal temperature range of maybe 10 percent of the equilibrium temperature, the simple radiative convective model of Cao et al. shows fairly large decreases. I really think that there's some question whether a GCM can be expected to reproduce the diurnal cycle, given the type of land-surface physics involved.