We have recently investigated a series of compounds based on the Cr(V) tetraperoxides (general formulas M3CrO8 where M=Li, Na, K, Rb, Cs) that exhibit novel magnetic and heat capacity properties. Chief among them is the promise of superior performance for magnetic refrigeration. Currently, adiabatic demagnetization refrigeration (ADR) compounds are generally limited in their effective cooling temperature range. These limitations are a function of the magnetic spin ordering temperature, which limits the lowest attainable temperature, and the spin concentration, which limits the refrigeration power. Our investigations indicate that the peroxychromates can be tuned to possess maximal refrigeration power at a desired operating temperature. Evidence for this claim is suggested by the heat capacity coefficient (b). The lower the magnitude of b, the greater the ADR potential. Experimental evidence shows introducing larger cations significantly lowers b, while basically maintaining the spin concentration. This paper focuses on explaining the trend in terms of contributions to the internal fields, which are tentatively assigned to the exchange and dipolar interactions. It is predicted that the controlled modification of these fields by molecular structural alterations tunes these compounds to have maximum refrigeration power over a broad range of temperatures, i.e., 0.010 to 20 K.