We report the synthesis of monomeric and dimeric dicyanovinylbenzothiadiazole-based non-fullerene acceptors and investigate the phase behavior of blend systems comprising poly(3-n-hexylthiophene) (P3HT) and the new materials. Differential scanning calorimetry (DSC) thermograms of blends with different compositions revealed that no eutectic composition existed for the blends, in contrast to previously reported P3HT/non-fullerene acceptor combinations. Analysis of the DSC data shows that the thermal properties of the P3HT and the dimeric non-fullerene acceptor are almost independent of blend composition. However, the thermal properties of blends containing the monomeric acceptor were found to depend strongly on the blend composition, with increasing concentrations of the monomeric acceptor depressing the observed melting point of the polymer. These results are complemented by specular X-ray diffraction data, which reveals stark differences in the crystallinity of the two blend systems. In the case of the dimeric acceptor, the polymer and non-fullerene molecules crystallize in a form similar to that of the neat compounds, whereas in the case of the monomeric acceptor the crystallinity of both molecules is substantially altered by the other. We then correlate the structure of the materials with the organic solar cell performance.