If the earth had a thinner (fewer gas molecule) atmosphere, how would the temperature change? Why

Would it be less hot in a desert during the day or would it be even hotter then normal ? How would the desert nights change?

If the atmosphere was thinner then there would be two changes at work. The first is that it would be hotter during the day and colder during the night, if there was no atmosphere then the day/night difference could easily be 200C or more. The other effect is that the atmosphere holds heat in and keeps the average temperature higher than it would be without an atmosphere.

With no atmosphere the daytime temperature of the Moon can be 120C and the night time can drop to -200C. Because the earth rotates faster it wouldn't be as extreme as it is with the Moon's month long day but the less air you have the closer you move to conditions like those.

It would actually be hotter with the sun shining down, as there'd be less atmosphere to disperse the heat delivered by sunlight. At night, instead of acting like a blanket, holding in some of the sun's heat, it would cool off very rapidly - and temperatures would drop more dramatically than they do now.

(Consider the moon: a *very* thin atmosphere, and it's 200 degrees on the day side, and 250 below on the shadowed side...)