In the previous Halachot we have discussed that one may not hang up a wet garment in order to dry it on Shabbat.
Let us now discuss a situation where a garment becomes wet in whatever manner, such as a raincoat becoming wet from the rain, and one wishes to dry this garment on Shabbat. Is this permissible or not?
We have already explained that the underlying reason behind the prohibition of spreading out clothing in order to dry it on Shabbat is because we are concerned about people suspecting the one drying the clothing on Shabbat that he laundered the clothing on Shabbat as well. Thus, regarding our scenario, one may dry the garment by placing it down in a way that it is not noticeable that one intends to dry it, such as by hanging it on the back of a chair, for many people hang their coats up this way all the time and no one will suspect him of laundering on Shabbat. It is therefore permissible to dry a garment in this way.
Drying Clothing Next to a Heat Source
Many people customarily place clothing next to a furnace, radiator, and the like in order to have it dry quickly but this is a mistake as this is completely forbidden, for the water absorbed in the garment evaporates as a result of the heat the furnace and as such, it is quite possible that the water will reach a temperature at which the hand recoils (over 104 degrees Fahrenheit) which constitutes the Torah prohibition of cooking on Shabbat. It is therefore absolutely forbidden to place a wet garment next to a heat source on Shabbat. There is only room for leniency when the water cannot reach this temperature.
It is also common for people to hang laundry on designated hanging devices meant for laundry and once the garments are already hanging there, some just move the hanging apparatus slightly towards the heat source in order to speed up the drying process. This is likewise completely forbidden based on what we have written above.
Summary: A garment that became wet on Shabbat in whatever manner may be hung on a chair and the like in a way that it is unnoticeable that one intends to dry it. It is absolutely forbidden to place a wet garment next to a space heater or radiator in order to dry it on Shabbat.