Clay slurries are both ubiquitous and essential in the oil exploration industry, and are most commonly employed as drilling fluids. Due to its natural abundance, bentonite clay is often the de facto choice for these materials. Understanding and predicting the mechanical response of these fluids is critical for safe and efficient drilling operations. However, rheological modeling of bentonite clay suspensions is complicated by the fact that thermally-driven microscopic arrangements of particle aggregates lead to a continual evolution of the viscoelastic properties and the yield stress of the suspension with time. Ergodic relations fundamental to linear viscoelastic theory, such as the Boltzmann superposition principle, do not hold in this scenario of 'rheological aging'. We present an approach for modeling the linear viscoelastic response of aging bentonite suspensions across a range of temperatures that is based on the transformation from laboratory time to an effective 'material time' domain in which time-translation invariance holds, and the typical relations of non-aging linear viscoelastic theory apply. In particular, we model the constitutive relationship between stress and strain-rate in the bentonite suspensions as fractional Maxwell gels with constant relaxation dynamics in the material time domain, in parallel with a non-aging Newtonian viscous contribution to the total stress. This approach is supported by experimental measurements of the stress relaxation and rapid time-resolved measurements of the linear viscoelastic properties performed using optimized exponential chirps. This data is then reduced to master curves in the material domain using time-age-time superposition to obtain best fits of the model parameters over a range of operating temperatures.