I spent most of this weekend calculating solar elevations at different latitudes and different times of the day, which involved a lot of messing about with sines, cosines and tangents (and a lot of simplifications and sensible assumptions, which you have to test back and forth until you get plausible results).
After I finally got the spreadsheet to work, I did a 'daily radiation budget' or 'climate model' for somewhere at latitude 45N close to sea level (which happens to be Bordeaux, France). 45N or 45S is a good place to start because at that altitude you know that solar insolation is precisely the average for the whole planet. After more tweaks, I got daily high, low and average temperatures to match up perfectly for the month of September, which is the month of the autumn solstice. Arguably, this overstates temperatures because it's still warm from the summer; but the model also overstates temperatures because I ignored the +/- 23 degree wobble of the earth, and the two effects seem to cancel each other out.
I did one tab for ground level and the boundary layer (the lowest 500m of atmosphere, where the temperature is similar to ground level) and the next tab for Bordeax plus the column of troposphere above it (10 km up), both as adjusted for the gravito-thermal effect. They reconcile nicely with each other.
The main lesson here is that you have to make endless assumptions for albedo and emissivity and so on (starting with traditional assumptions and tweaking) and you can only get the starting temperature by trial and error - if you set it too high, you get too much outgoing radiation, which indicates cooling as incoming solar radiation is fixed (and vice versa). If you change albedo or emissivity by one percent, you get an additional degree of warming or cooling. You can firm up on these tweaks and assumptions, I suppose, but in doing so, you would have to make more tweaks and assumptions to resolve the uncertainty; and more tweaks and assumptions to resolve those... until you end up with a house of cards ready to collapse at the slightest peturbation.