Solid single-Li+-ion conducting polymer electrolytes are currently explored for safe high-temperature lithium batteries. In the present work we have prepared and studied materials based on alternating mesogen-like naphthalene sulfonate units interconnected by flexible poly(ethylene oxide) (PEO) segments in order to induce microphase separation and physical crosslinking. These segmented polymers were readily prepared in polycondensations of a naphthalene diol sulfonate and chain-end chlorinated PEO. The ionic content of the final materials was conveniently controlled by using PEOs of different molecular weights. Analysis by X-ray scattering showed a morphology with nanoscopic domains of naphthalene sulfonate units dispersed in a matrix of amorphous PEO segments. The aggregation of the naphthalene sulfonate units increased with temperature up to at least 100 degrees C, while the crystallization of the PEO segments in some materials reversibly dissolved the naphthalene sulfonate domains upon cooling. The crystallinity decreased and the glass transition temperature increased with decreasing PEO molecular weight, i.e., increasing in ionic content, because of increasing ionic coordination and a decreasing PEO segment length in-between the naphthalene sulfonate domains. At 80 and 120 degrees C, the present single-Li+-ion conductors reached conductivities up to 1.4.10(-6) and 5.5.10(-6) S cm(-1), respectively, which after addition of 29 wt % triglyme increased to 2.9.10(-6) and 8.2.10(-6) S cm(-1), respectively. The combined results showed that the macromolecular design with ionic mesogen-like units that form stable physically cross-linked morphologies by interconnecting flexible polyether segments is advantageous for polymer electrolytes for safe high-temperature operation.