The viscoelastic properties and ionic conductivity of ion gels based on the self-assembly of a poly(styrene-b-ethylene oxide-b-styrene) (SOS) triblock copolymer (M(n,S) = 3 kDa, M(n, O) = 35 kDa) in the ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amide ([EMI][TESA]) were investigated over the composition range of 10-50 wt % SOS and the temperature range of 25-160 degrees C. The poly(styrene) (PS) end-blocks associate into micelles, whereas the poly(ethylene oxide) (PEO) midblocks are well-solvated by this ionic liquid. The ion gel with 10 wt % SOS melts at 54 degrees C, with the longest relaxation time exhibiting a similar temperature dependence to that of the viscosity of bulk PS. However, the actual values of the gel relaxation time are more than 4 orders of magnitude larger than the relaxation time of bulk PS. This is attributed to the thermodynamic penalty of pulling PS end-blocks through the PEO/[EMI][TESA] matrix. Ion gels with 20-50 wt % SOS do not melt and show two plateaus in the storage modulus over the temperature and frequency ranges measured. The one at higher frequencies is that of an entangled network of PEO strands with PS cross-links; the modulus displays a quadratic dependence on polymer weight fraction and agrees with the prediction of linear viscoelastic theory assuming half of the PEO chains are elastically effective. The frequency that separates the two plateaus, omega, reflects the time scale of PS end-block pull-out. The other plateau at lower frequencies is that of a congested micelle solution with PS cores and PEO coronas, which has a power law dependence on domain spacing similar to diblock melts. The ionic conductivity of the ion gels is compared to PEO homopolymer solutions at similar polymer concentrations; the conductivity is reduced by a factor of 2.1 or less, decreases with increasing PS volume fraction, and follows predictions based on a simple obstruction model. Our collective results allow the formulation of basic design considerations for optimizing the mechanical properties, thermal stability, and ionic conductivity of these gels.