A unified thermodynamic treatment is presented for reorientation transitions in ultrathin ferromagnetic films, driven by temperature or thickness variations. Since the physical mechanism underlying such transitions is the competition between surface, bulk, and shape anisotropy, the natural and proper scenery to examine the problem is the anisotropy space of the corresponding system. The recently developed anisotropy-flow concept is then applied to detect and characterize the possible thickness- and temperature-driven reorientation transitions, consistent with the standard, though not universally valid, assumption for the additive separation of the bulk and surface contributions. Three generic types of transition are easily identified with a number of subcases each. Each generic scenario is seen to come about as a simple consequence of the route which the system follows in the anisotropy space under variations of the driving parameter. The relevant characteristic thicknesses are easily identified. We find that, as a rule, there exist two borderlines in the ferromagnetic part of the T-d diagram of the system; these should lead in principle to a much richer structure of the diagram in question than has been reported so far.