Crystal structures of the high-temperature phases of odd-numbered fatty acids (C(n)H(2n-1)OOH) from tridecanoic acid (C(13)H(25)OOH) to tricosanoic acid (C(23)H(45)OOH) are presented in this article. They have been determined from high-quality X-ray powder-diffraction patterns. Two types of high-temperature phases are adopted: one monoclinic A2/a with Z=8 for the fatty acids with n=13 and n=15, denoted as C'', and one monoclinic P2(1)/a with Z=4 for the longer-chain fatty acids, denoted as C'. It appears that the packing arrangement of the alkyl chains and of the carboxyl groups is similar in all of the structures. However, the arrangement at the methyl-group interface differs between the C' and C'' forms. A survey of the intermolecular interactions involved in these polymorphs coupled with a study of the effects of temperature on the structures have led us to a better understanding of the arrangement of the molecules within the high-temperature solid phases of odd-numbered fatty acids.