Puffy upper eyelids do not go down with hot compresses as seen in a variety of conditions. Firstly, not all puffiness can be relieved by hot compresses and some need to be treated with cold compresses, such as various infectious diseases other than wheals.
Secondly, swelling may be caused by a systemic disease, and if the primary disease, such as kidney disease or heart disease, is not actively treated, hot compresses will not usually have a significant effect. If the upper eyelid swelling does not improve with treatment on its own, it is recommended that the cause is identified in hospital and treated regularly as prescribed.