[The sun by its self is not warming the earth from -273 deg C to what we have today.]
According to the Apollo 14 mission report, the maximum temperature during lunar day is 1360 F and the minimum temperature during lunar night is minus 110 F.
The temperature differential is entirely due to the alternating presence and absence of solar radiation.
+225 degree Fahrenheit during the day is more like it. But you are correct there is a huge difference when there is no atmosphere. All radiated heat makes it to the surface.