Within the linear tetrahedron method, the term is interpolated linearly between two k-points. Bloechel  has recently revised the tetrahedron method to give effective weights for each band and k-point. In addition Bloechel was able to derive an correction formula which removes the quadratic error inherent in the linear tetrahedron method (linear tetrahedron method with Bloechel corrections). The linear tetrahedron is more or less fool prove and requires a minimal interference of the user.
The main drawback is that the Bloechels method is not variational with respect to the partial occupancies if the correction terms are included, therefore the calculated forces might be wrong by a few percent. If accurate forces are required we recommend a finite temperature method.