A therapeutic device such as an eye mask or compress for delivery of moist heat therapy to a body part such as an eye of a human or animal subject. Example devices are configured to be worn with one or more eye coverage portions positioned over the subject's eye(s). The eye coverage portions have a front side configured for placement against the treated body part, and a back side opposite the front side. The eye coverage portions include recesses or retracted sections configured to be positioned over the wearer's cornea area. The shell of the eye coverage portions may further incorporate antimicrobial properties. Heat transfer mediums or fill materials can include hydrophilic zeolite, silica gel, and/or one or more phase change materials so as to provide controlled performance characteristics.