Aqueous dispersions of homo- and copolymer microgels of N-isopropylacrylamide (NiPAm) and N,N-diethylacrylamide (DEAm) with different compositions are temperature-dependently studied by means of proton nuclear magnetic resonance spectroscopy (H-1 NMR) and differential scanning calorimetry (DSC). Furthermore, the effect of varying the solvent composition by adding methanol is investigated. Methanol addition leads to a broadening of the thermally induced volume phase transition in case of NiPAm-containing samples, as confirmed by DSC. At the same time, the width of transition approaches the one of neat PDEAm. Two different solvent species, namely bulk-like and restricted solvent, are observed as separate lines in H-1 NMR experiments when the gels deswell. The restricted nature of the second species is affirmed by pulsed field gradient (PFG) NMR self-diffusion experiments. The temperature T-split, from which on the restricted species is found cannot be directly related to the volume phase transition temperature determined by DSC. The difference between T-split and the DSC peak temperature changes depending on the NiPAm-content of the microgel. An increase in the shift difference between the two solvent signals with temperature indicates a continuous change of the restricted solvent environment. At even higher temperature, the shift difference of restricted and bulk solvent approaches asymptotically a constant value. In general, the observed effects of methanol addition are consistent with an increasing complexation of the amide protons of the microgel (originating from the NiPAm units) with methanol. In contrast, poly(DEAm) does not show any anomaly concerning transition width and T-split upon methanol addition. This is attributed to the lack of amide protons. The results indicate that the presence of cononsolvency can be explained by the presence of the amide proton.