ah, I have a solution for that. too,
First, don't melt it to get it in, just soften it enough to be able to mould it wth a spoon.
Use about 1/3 cup of cold water with a bit of salt, maybe 1/4 teaspoon.
Once you put the part with the butter upside down in the part with the water, you have an air seal.
Now, set the whole thing in a shallow pan (I use an old pie plate) with water in it and put it in the shade by an open window.
Stays fairly cool from evaporation. If you need more cooling, wrap it in a wet dish towel.