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Could you be thinking of The First Men in the Moon? They travelled there by a cramped sphere. Being trapped outside, having lost the sphere as the temperature changed and needing to seek shelter was a plot point. There were different types of Selenites who did have large heads. As I recall, they were more specialised than directly competitive against each other (being a kind of caste system with different appearances and abilities) so this may not be a perfect fit.
Edited by ApeAccount

I vaguely remeber a short passage from some old novel, where there was an expedition to Moon. There were at least two different kinds of sapient aliens who somehow competed against each other. Then I remember the human landing pod which was spherical and rather cramped. The protagonist needed to take shelter there during lunar night due to extreme cold (or day due to extreme heat? I don't remember. It was over 25 years ago, since I read it and the novel was probably even older.)