I find it puzzling that Moon's maximum "daily" equatorial temperature is almost 400K. Earth's theoretical black body temperature would be 279K at 1AU, and Moon is the same distance from Sun, yet its equatorial temperature is well over 100K hotter than Earth's. Thoughts on this?
How did you come up with the black body temperature of 279K? That's plain false. The solar radiation above the atmosphere is approx. $1.4kW/m^2$ and the black body temperature of that is around 400K, which is approx. right. Did you happen to use the AVERAGE thermodynamic temperature for a quickly rotating body at 1AU? That would be around the 279K, if I am not mistaken. Clearly that approximation doesn't apply to the max. temperature of the lunar soil.
I'm not familiar with the math, but am wondering if the 4 should be a 2 instead, (for hemisphere).
The Moon's day is about 13.5 of our days, so at its highest the lit side and dark side of the Moon can vary up to 500 degrees F, from about 250F on the lit side to about -250F on the dark side.
I would suggest that our atmosphere - which is literally mass itself - (though it is mostly invisible so a lot of people don't think of it as mass) - none the less it is mass - among other factors this mass acts as a thermal blanket to equalize the temperatures - thus causing things like hot/cold convection currents, winds and storms to occur which are not normally seen on the moon. The moon does not have a similar atmosphere, though studies are now suggesting it does have certain atmospheric gasses - they are not the same type and do not have the same affects as our atmosphere on Earth.
Its very simple, there are no atmospheric layers, no air and the surface is not similar like earth. Complex carbonaceous matter present on the lunar surface is cool and have no ability to absorb heat. when hot sun rays directly strike to lunar surface it become warm according the intensity of sun rays and when there are no rays it cool down to its own original temperature.