The alternating sequenced copolymer poly-(methacrylic acid-alt-hydroxyethyl acrylate), p(MAA-alt-HEA), was recently found to display a lower critical solution temperature (LCST) behavior in 1,2-dimethoxyethane (DME), whereas the random copolymer of the same average molecular weight and composition did not. As an effort to understand this peculiar behavior, we investigated solutions of both corresponding homopolymers, poly(methacrylic acid) (pMAA) and poly(2-hydroxyethyl acrylate) (pHEA), in DME. We found that in the same temperature range, concentration, and degree of polymerization, pHEA is fully soluble, whereas pMAA shows the LCST behavior similar to the alternating copolymer. On the basis of Hansen's parameters of the homopolymers, it would be predicted that neither should dissolve in DME. Solubility is therefore connected to specific solvent-polymer interactions and more specifically to the formation of a polymer-solvent complex via hydrogen bonds. We designed a method which combines mid-infrared (MIR) and near-infrared (NIR) spectroscopy in solution to study hydrogen bonding as a function of temperature (by MIR) with simultaneous monitoring of LCST (by NIR). In parallel, the global shape of polymer chains and aggregates was characterized by small-angle neutron scattering in deuterated DME. It is found that pMAA chains form aggregates upon increase of temperature through formation of cyclic H-bonded dicarboxylic dimers. As for pHEA, the solvent's quality of DME slightly decreases with temperature, but aggregation is prevented by entropic repulsion of the flexible side chains. We thus concluded that nonoccurrence of LCST in the random copolymer is due to the presence of pHEA homoblocks that maintain constant solubility over the whole temperature range.