In accordance with certain illustrative embodiments, methods and apparatuses of treating obstructive disorders of the structure of an eye or eyelid are disclosed. The treating may involve applying heat to the structure containing the obstructive disorder to melt an obstruction in the structure and place the obstruction in a melted state. The heat may be maintained for a time period to melt the obstruction and place the obstruction in the melted state. The structure may be treated by expressing the melted obstruction from the structure. The treating may be carried out either during the time period or after the time period when heat is applied but while the obstruction is in the melted state. In certain embodiments, the method further involves subsequently treating the structure by use of a pharmacological agent. This abstract is not to be considered limiting, since other embodiments may deviate from the features described in this abstract.