The most common way to clean and sanitize water is through heating, either boiling it or distilling it. Either method leaves your water hot. This is fine if you want to make coffee right away and don't ever drink plain water. Most people will want to drink plain water some of the time. Hot or warm water is not great most of the time.
If you are using plastic containers to store your water, you may need to cool the water before placing it in your containers. I use plastic containers to store my water that I intend to drink for the next day or so. The bottles are tough enough not to completely melt with hot water in them, but they will warp and then leak.
I used to always boil my water before I filtered it through a fancy ceramic filter with silver in it. That was to make the filters last longer by not loading them up with extra contaminants. The idea of breaking that filter by putting hot water on it was not good. I cooled it first. I used large metal bowls to cool the water. Once the water was cooled, I poured it into the filter.
It was impossible to keep flies and gnats out of my home. There were a lot of them in the town I lived in. Before the water in my bowls cooled it would have insect bodies floating in it.
I tried putting tea towels over the bowls, but it was hard to keep them on the bowls tight enough to keep all insects out. I tried using giant rubber bands over the tea towels or tying strings around them. Since the bowls were round, curved, and slippery, getting strings or rubber bands over them plus a tea towel was a challenge.
It was too much of a challenge to tie down tea towels so often. I decided to make bowl covers that would slip easily over the bowls and that would fit tightly over them.
Elastic with a casing was my method for getting the bowl covers on and off easily. I traced around the bowls onto a piece of paper to make patterns for the bowl covers. I tripled the width of the elastic and added that to the width of the bowl covers. I did a pencil and string compass and got the exact measurements at first, but found it wasn't necessary.
It works fine to just look around the house for something a little bigger than the top of the bowl. It needs to be round, or the same shape as the bowl top and bigger than three times the width of the elastic plus the bowl width. The cover can go way down the side of the bowl and still work.
Smaller than three times the width of the top of the bowl is not a good idea. It can be done, but it is a lot of extra work. If you have to do that, you will need to do something to prevent the fabric from unravelling along the edge.
A zigzag machine stitch works if you have a sewing machine. If you don't have a sewing machine you can use a whip stitch or blanket stitch along the edge of the fabric.
I do not think you should use anything like Fray Check or other fabric glues on your bowl cover. I believe that could contaminate your water.
You can find out how much elastic you need for your bowl cover by tying a string around the top of your cooling bowl and then measuring the string. You need to add a little extra to allow for overlapping the edges of the elastic after you insert it in your casing.I think triple the width of the elastic is a good amount of overlap.
Your casing needs to be slightly wider than your elastic when it is folded over. You need to allow for the width of your seam as well. If you don't have tailor's chalk, regular chalk or a pencil will do to mark where to put your seam. Colored regular chalk may permanently stain your fabric. I would not use a pen, for fear of water contamination.
If you are not planning to machine sew the edges of your bowl cover fabric, you will need to hem it before you sew the casing. That is why it needs to be triple the width of the elastic, or wider.
You can make your own seam gauge if you don't have one. A piece of cardboard marked with the seam width will work. Mark your seam at frequent intervals all around the bowl cover edge. If you have not sewn much or are a perfectionist, you should mark a solid line for your seam all the way around the bowl cover. It is easier to keep your seam straighter that way. Mark it on the wrong side of your fabric so it won't show when you are done.
You can pin or baste your casing before you sew it. It is much easier to get it straight that way when you sew it.
Leave a small gap before you sew all the way around your elastic casing. You will need a gap to put the elastic in. Put a safety pin, that is about the size of the width of the elastic, through the end of the elastic. That makes it much easier to thread the elastic through the casing. You can also use a paper clip, if you don't have a safety pin. Pin the dangling end of the elastic to the fabric, before you begin threading the other end with the safety pin or paper clip in it. That keeps the non-threading end from being pulled inside the casing and getting lost.
After you thread the elastic through the casing, check to make sure there are no kinks in the elastic. If there are kinks, untwist them, so the elastic is flat all the way around. Once you have the elastic inside the casing you need to sew the two ends of the elastic closed so that it forms a continuous loop inside the casing. Next close the gap that you used to get the elastic into the casing. You can use a machine or do it by hand.
Once your gap is closed your casing is done. I like to wash a newly made bowl cover before I use it the first time. When your bowl cover is clean it is ready to use.
Once your bowl cover is ready, pick it up with both hands on opposite sides of the elastic. Place the part of the bowl cover that is in front of you and between your hands against the edge of the bowl and under the rim of the bowl. Stretch it away from you towards the side of the bowl away from you. Slip it over the rim on the other side of the bowl and release the elastic under the rim of the bowl.
You may want to practice putting on the bowl cover with the cooling bowl empty a few times before you do it with water in it. It won't matter if the cooling bowl cover gets wet when you put it over the water in the bowl. It will still keep out dust and insects even when it is wet.
I have made cooling bowl covers out of plastic for use in the refrigerator. I dislike "refrigerator taste" in my food, so the plastic covers help prevent that.
Cooling bowl covers are also good for picnics and potlucks. I prefer to make mine out of see through fabric. I know how much water is in the bowl that way, but they seem cleaner to me than solid ones. There is no particular reason it has to be that way though. You could use whatever you want or have handy.
I am going to add drawings of how to make cooling bowl covers to make it easier for those who are not used to sewing.