For your oils, don't heat them unnecessarily. I put my soap pan on the stove, add my oils and fats, then stick a roast thermometer in and turn on the heat for only long enough that the solid fats start to melt. Then I turn off the heat (remove the pan if you have an electric stove) and go add the lye to the water. A few minutes later I stir the oils to see if the solids have all melted, and if not I give it a short amount more heat. Don't let your oils and fats get above 120 degrees and you won't need to wait as long for them to cool off. There is no reason to get them hotter than 120.
Your lye will take longer to cool off, depending on the container etc. I use a Pyrex glass measuring cup. To speed things up start out with some ice cubes when you are measuring your water. (The cubes are part of your water weight.) I suggest about 1/4 to 1/3 the water weight in ice, but not too much or your lye mixture won't heat enough to dissolve the lye correctly. The other way to cool it faster is to partially fill your sink with 2-3 inches water and add some ice cubes. Mix your lye and water, then sit the container in the ice water bath and observe the temperature on a thermometer. Remove from ice bath when you are nearing your target temperature.
Paprika is not saponifiable, is not a fat, and does not enter into lye calculations. And beware adding too much or you'll get paprika colored lather which is the definitive sign that too much colorant was used. I'm not using natural colorants anymore but I suggest that a limit might be 1 teaspoon paprika per pound of oils, or maybe up to 1 tablespoon but I'm not sure that may be too much. Perhaps somebody more experienced may add to my comment.
