Keep in mind that one of the most basic attributes of oil-filled heaters is that they are simply inherently safe, including having people, even babies and pets, touch them. They don't and can't get all that hot. Towels and other fabrics get hotter in clothes dryers. Cotton is composed of cellulose, like paper, wood, etc. and will start to combust/burn until mid-400s˚F, with melting point even higher. I doubt any oil-filled heater even gets up to 140˚F, or else people would commonly get burned by them. Many times I've dried pieces of wet clothing (including synthetics with melting points way lower than cellulose combustion point) on an oil-filled heater with no problems.
Bottom line -- Draping wet, or even dry, towels or other fabric over an oil-filled heater is way safe, zero risk.
