The use of dipolar shifts as important constraints in refining molecular structure of paramagnetic metalloproteins by solution NMR is now well established. A crucial initial step in this procedure is the determination of the orientation. of the anisotropic paramagnetic susceptibility tensor in the molecular frame which is generated interactively with the structure refinement. The use of dipolar shifts as constraints demands knowledge of the diamagnetic shift. which, however, is very often not directly and easily accessible. We demonstrate that temperature gradients of dipolar shifts can serve as alternative constraints for determining the orientation of the magnetic axes, thereby eliminating the need to estimate the diamagnetic shifts. This approach is tested on low-spin, ferric sperm whale cyanometmyoglobin by determining the orientation, anisotropies and anisotropy temperature gradients by the alternate routes of using dipolar shifts and dipolar shift gradients as constraints. The alternate routes ultimately lead to very similar orientation of the magnetic axes, magnetic anisotropies and magnetic anisotropy temperature gradients which, by inference, would lead to an equally valid description of the molecular structure. It is expected that the use of the dipolar shift temperature gradients, rather than the dipolar shifts directly, as constraints will provide an accurate shortcut in a solution structure determination of a paramagnetic metalloprotein.