Using simultaneous synchrotron small- and wide-angle X-ray diffraction (SWAXD), we investigated the thermotropic behavior of a cationic lipid mixture of DOTAP-DOPC (1,2-dioleoyl-3-trimethylammonium-propane-dioleoylphosphatidylcholine) liposomes complexed with calf thymus DNA. The DOTAP-DOPC/DNA complex reacts to temperature change by a bilayer compression normal to its surface and an expansion of the DNA in the plane of the rod lattice. By applying two independent recently developed models, we show here for the first time that the thermotropic dilatation area of lipid headgroups within the complexes is not isotropic but occurs parallel to the 1D DNA lattice (i.e., along the direction perpendicular to the DNA axis). Our results shed light on the role of spatial dimensionality in the DNA packing density within lamellar lipoplexes and provide experimental evidence that the interaction between DNA molecules confined between lipid bilayers can be regarded as a 1D problem.