Another factor which contributes to the magnitude of the diagonal elements is the size of the B value of the atom. Atoms with high B values have smaller diagonal elements for all their parameters. These atoms will be under shifted in Conjugate Gradient refinement. Since usually atoms are created with small B values and are under shifted in each cycle they will never reach their correct location nor will their thermal parameters become as large as required by the observations.
Atoms with large B values almost certainly should have even larger ones. Again, a method which uses the diagonal elements will not exhibit this problem. However, most programs which do utilize the diagonal elements of the normal matrix calculate them with the approximation that only the element type of the atom is important. They ignore the contribution of the B value to these terms. This is done for historical reasons. In small molecule structures, where refinement was originally developed, there usually are no atoms with particularly large B values, and the assumption is good. The early protein refinement packages made the same assumption without reconsidering its validity.
Therefore some programs will underestimate the thermal factors even when using the diagonal elements. To learn if this is a problem in your refinement you must discover exactly how these matrix elements are calculated. Usually this is not an easy task. The program's source code must be examined.