It depends on your oils and what temperature they start to harden. And if you are using milks, which may or not be frozen prior to using in the lye solution.
If I soap too cold with hard oils, I can end up with false trace. And before I realized that was what was happening, I started coloring and so forth, then as the lye began to heat up the oils again, the batter got thin and started to separate. I was able to save that batch, but it could have been avoided by soaping at a temperature above the melting point of the hard oils in the recipe.
Once I used frozen milk to make my lye solution and apparently did not stir enough to keep the lye from coming out of solution (or maybe I only thought it was fully dissolved, I am not really sure). I also kept the container in an ice bath to keep the temperature down because I wanted to prevent the milk from scorching. The solution was so cold that the lye had clumps in it. I was so inexperienced and probably too tired or something (not sure what my problem was that day, but I missed an obvious clue! - the clumps in the lye solution) and went ahead and soaped anyway, clumps and all. I erroneously thought 1. that the clumps were frozen solution that was sufficiently dissolved, and 2. that even if part of the clumps had 'precipitated out of solution' that when they got together with the oils that the resulting heat would re-dissolve the clumps. Big mistake! The oils were cool, the lye solution was COLD. The clumps never un-clumped and ended up as solid lye clumps in my soap. They looked like rock crystals.
Don't do what I did and lick a solid piece of crystal in your soap! It took my tongue at least a week before it began to feel even close to normal again!
There are probably other factors to consider as well, but those are the ones that are most obvious to me from my experience.
