We present a mean field study on the R6Fe23 system, where R = Dy, Ho, Er, and Tm, to calculate the magnetization, magnetic heat capacity, and the magnetocaloric effect (MCE) (isothermal entropy change (ΔSm) and the adiabatic temperature change (ΔTad)) for different field changes up to 5 T and at temperatures ranging from 0 to 600 K. The maximum ΔSm, using the trapezoidal method, for the R6Fe23 system is in the range 4.9–9.8 J/K mol, and the maximum ΔTad is in the range 9.56–15.17 K for a field change ΔH = 5 T. The largest ΔSm and largest ΔTad are found for Tm6Fe23 to be 9.8 J/K mol and 15.17 K at Curie temperature Tc = 489 K, for ΔH = 5 T. The relative cooling power RCP(S) is in the range 148–560 J/mol for ΔH = 5 T, which is comparable to that of bench-mark materials, e.g., Gd. Also, the RCP based on the adiabatic temperature change, RCP(T) is in the range 449–1092 K2 for ΔH = 5 T, which is comparable also to that of bench-mark materials, e.g., Gd. We investigated the type of phase transition in the light of universal curves, Arrott plots, and the behavior of the magnetic moment, magnetic heat capacity, and MCE (ΔSm, ΔTad), which confirm that the type of phase transition at Tc of this system is second-order phase transition (SOPT). A calculation of some critical exponents adds more evidence that the MFT is fairly suitable to handle the aforementioned properties in the studied systems.