The crystal structure of the spin-canted antiferromagnet beta-p-NCC(6)F(4)CNSSN* at 12 K (reported in this work) was found to adopt the same orthorhombic space group as that previously determined at 160 K. The change in the magnetic properties of these two crystal structures has been rigorously studied by applying a first-principles bottom-up procedure above and below the magnetic transition temperature (36 K). Calculations of the magnetic exchange pathways on the 160 K structure reveal only one significant exchange coupling (J(d1)=-33.8 cm(-1)), which generates a three-dimensional diamond-like magnetic topology within the crystal. The computed magnetic susceptibility, chi(T), which was determined by using this magnetic topology, quantitatively reproduces the experimental features observed above 36 K. Owing to the anisotropic contraction of the crystal lattice, both the geometry of the intermolecular contacts at 12 K and the microscopic J(AB) radical-radical magnetic interactions change: the J(d1) radical-radical interaction becomes even more antiferromagnetic (-43.2 cm(-1)) and two additional ferromagnetic interactions appear (+7.6 and +7.3 cm(-1)). Consequently, the magnetic topologies of the 12 and 160 K structures differ: the 12 K magnetic topology exhibits two ferromagnetic sublattices that are antiferromagnetically coupled. The chi(T) curve, computed below 36 K at the limit of zero magnetic field by using the 12 K magnetic topology, reproduces the shape of the residual magnetic susceptibility (having subtracted the contribution to the magnetization arising from spin canting). The evolution of these two ferromagnetic J(AB) contributions explains the change in the slope of the residual magnetic susceptibility in the low-temperature region.