A container has an impermeable outer membrane sized to fit generally within the peri-orbital region and sufficiently flexible to mold to the structure of the closed eye. Heat which is generated by an exothermic reaction inside the container, which provides steady-state heat to the eyelids. A soft, non-abrasive, lint-free material is presoaked in a pH controlled (preferably antibacterial and hypoallergenic) detergent, with or without an ophthalmic antibiotic solution. The compress may also have a handle which makes holding and maneuvering the compress more feasible, while protecting the user's fingers from the heat, and preventing the contamination of the compress by the fingers. The compress may be packed in a watertight, sterile wrapper which will prevent drying of the detergent solution. Other embodiments are also described and claimed.