Fillers such as Radiesse eventually dissolve, but this can take a long time in certain areas of the face such as the nose. By "a long time" I mean 2 years or occasionally longer.
Hyaluronic acid gels, on the other hand (Juvederm, Restylane, Perlane, etc.), not only dissolve and resorb more quickly, but if need be their dissolution can be sped up with the injection of hyaluronidase, an enzyme that breaks down hyaluronic acid. This property makes HA fillers very forgiving.
Non-resorbable fillers, such as Artefill--as the term implies--do not resorb or go away. This is both good and bad, depending on what it's used for in the nose and how it's applied.
Certainly if someone is considering a revision surgical rhinoplasty and has a temporary filler (Radiesse, Juvederm, etc.), it's very important that the filler is completely dissolved before surgery so that an accurate revision can be done.
All the best,