Why are there temperature differences on the moons surface even though there is no atmosphere present?
In the absence of conduction and atmospheric convection, heating and cooling is dominated by radiation. This is the dominant effect in the heating of the Moon’s surface. Sunlight impinges on the surface, some is reflected, and some is absorbed. The surface also radiates in the infrared. The balance of these energy flows determines the temperature.
It’s like the earth, at any point only half (maybe even lesser) of the Moon is facing the Sun, so the temperature there will be warmer because of heat from the Sun. And since there’s a really really thin atmosphere (or none at all), there’s no air to carry the heat around to the other side of the Moon. Therefore the temperature difference will be there, and the difference will be really really large.