In this study, a mathematical method was applied to establish modelling selection criteria for lumped parameter analysis (LPA), in the solid phase, of a diluted co-current moving bed heat exchanger (MBHE), with isothermal walls. Simplified expressions for particle temperature errors are obtained, showing, for certain parametric ranges, excellent agreement with the exact solution results. Another remarkable result is that for a MBHE with isothermal walls and very low particle Biot numbers, the possibility of steep intraparticle temperature gradients is demonstrated. Through a scale analysis, this behavior is explained, along with the physical foundations guiding the LPA selection criteria. The differences between two basic forms of approximation in MBHE modelling, that is, the uniform particle temperature assumption (UPTA) and LPA, are characterized. Also, new contributions are provided by the determination of parametric condition for the equality between the temperatures of the fluid and the particle surface and by limiting solutions. (C) 2019 Elsevier B.V. All rights reserved.