All models have limits but since the believers are familiar with MODTRAN it is kind of fun to use that to mess with their heads.
Assuming that "average" mean surface temperature is meaningful and 288.2 K degrees, if you hold everything else constant but increase surface temperature to 289.2 K degrees, according to MODTRAN there will be a 3.33 Wm-2 change in OLR at 70 km looking down.
Since the energy into the system is constant, the surface temperature should increase somewhat as the "benchmark" change in OLR at the TOA increases/decreases to restore the energy balance, but that assumes that there is no increase in clouds associated with the increase in surface temperature or increase in convection which both should provide a negative feedback.
Since we are most likely concerned with the "real" surface which should agree with the average global mean surface temperature, there will be less increase in temperature because there will be an increase in latent and sensible heat transfer to above the PBL.
Other than the "believers" that like to quote ancient texts (papers older than 5 years), there is a shift in the "consensus" to a lower sensitivity range but no one can put their finger on why. The simplest explanation is that someone screwed up in their hunt for the absolute worse possible case.
Whatever the case, an increase to 700 ppmv will likely produce less than a degree of warming at the real surface but could produce about 1.5 C degrees of warming or a range of ~0.75 C to 1.50 C degrees.