"To rinse with warm water" means to use water that is comfortably warm to clean or rinse something, typically to remove dirt or residue. Full definition
If you do get some in your eye simply wipe with a cotton pad then rinse with warm water until its cleared. (savvyhomemade.com)
To ensure good taste & texture, be sure to use enough water when boiling pasta and to rinse with warm water after draining. (chefdehome.com)
The instruction on this says to gently smooth onto face and neck after cleansing and to leave on for up to 10 minutes, then gently rinse with warm water. (facetocurls.com)