The Divertor Tokamak Test (DTT) facility is currently under design in Italy. This fully superconductive compact tokamak will be the test bench of several DEMO-relevant divertor solutions. The 4C code model of a DTT toroidal field magnet (including its structures) is developed here and used to support some important design decisions related to the neutron shield to be adopted, the need of an active cooling of the casing and the static heat load reduction. The simulations confirm the need to actively cool the casing by suitable cooling channels, but also the need of a proper neutron shield to reduce the nuclear heat load on the superconducting coils. On the other hand, the proposed static heat load reduction measures do not appear to be effective enough to satisfy the design requirement of 1.4 K for the minimum temperature margin.