An investigation on honeycomb solid matrix systems employed for high temperature thermal storage is provided numerically considering two models in the transient regime. The two models are related to a direct model with multiple channels and a porous medium model. The system with parallel squared section channels is described by a conjugated convective-conductive model by coupling the governing equations for fluid and solid matrix. The porous medium is modeled by assuming a Brinkman-Forchheimer-extended Darcy model and the LTNE is assumed. The models for different number of parallel squared channels or pores per unit of length (PPU) are considered. The honeycomb system is considered as an anisotropic porous medium, and assuming that the thermal storage system is adiabatic in order to estimate fluid dynamic and thermal characteristics for different PPU values. The Ansys-Fluent code is used to solve numerically the governing equations for both models. Results in terms of solid and fluid temperature profiles are given for different PPU values and for both models; they show that the two models are in very good agreement. The main consequence is that a honeycomb system can be simulated as a porous medium allowing a simpler numerical simulation also for parallel channel systems with high PPU. It is found that for high PPU systems the charging time decreases and for assigned partial charging time an increase in stored thermal energy is detected increasing the PPU value.