Polymer electrolytes show promise as alternatives to conventional electrolytes in energy storage and conversion devices but have been limited due to their inverse correlation between ionic conductivity and modulus. In this study, we examine surface morphology, linear viscoelastic, dielectric and diffusive properties of molecular ionic composites (MICs), materials produced through the combination of a rigid and charged double helical polymer, poly(2,2'-disulfonyl-4,4'-benzidine terephthalamide) (PBDT), and ionic liquids (ILs). To probe temperature extremes, we incorporate a non-crystallizable IL to allow measurements from -90 to 200 degrees C. As we increase the PBDT weight percentage, shear moduli increase and do not decay up to 200 degrees C while maintaining room temperature ionic conductivity within a factor of 2 of the neat IL. We connect diffusion coefficients of IL ions with ionic conductivity through the Haven ratio across a wide temperature range and analyze trends in ion transport based on a relatively high and composition-dependent static dielectric constant. This behavior may result from collective rearrangement of IL ions in these networks. We propose that these properties are driven by a two-phase system in MICs corresponding to IL-rich "puddles" and PBDT-IL associated "bundles" where IL ions form alternating sheaths of cations and anions around each PBDT rod. These polymer-based MIC electrolytes show great promise for use in electrochemical devices that require fast ion transport, high modulus, and a broad thermal window.