The role of the symmetrical conditions on the temperature field is studied in a capillary of rectangular geometry. By using the generalized flux, i.e., Robin-type of boundary conditions for the heat transfer in such a capillary domain, it is possible to identify clearly conditions under which the velocity field will depend crucially on the basic parameters and, therefore, what types of flow regimes may arise in the capillary channel. In addition, it is possible to conclude under what conditions the velocity field will not at all depend on some of these. The behavior is intimately tied to the symmetrical conditions associated with the temperature field in the system. A "skew" or asymmetrical parameter, W-infinity, has been identified in the temperature profiles; this parameter is useful for studying the role of the symmetrical conditions on the hydrodynamics field and in determining a set of a priori design criteria that limits the range of values of the parameters. Several numerical examples are presented to show the flow situations found in the system.