[en] The two-body correlation functions obtained in a lowest order constrained variational calculation for hot nuclear and matter, with the Reid potential and the explicit inclusion of Δ(1234), are state averaged and used to calculate the three-body cluster energy. The three-body cluster energy is found to vary between about 1 to 2 MeV through and beyond the twice nuclear matter saturation density for temperatures between 5 and 20 MeV. However the inclusion of three-body clusters does reduce the nuclear matter flashing and critical temperatures. A critical temperature of 14.8 MeV and a critical exponent of 0.347 are found. The results of entropy calculation are in good agreement with experimental predictions and other theoretical results. Finally it is shown that by allowing an explicit Δ(1234) degree of freedom through the Reid potential and including up to the three-body clusters, the LOVC calculation yields the other nuclear and neutron matter properties close to the available semi-empirical and experimental data at zero and finite temperatures