I'm actually not sure what temperature I soap at. Full disclosure up front is that due to some quirks in the heating system of the building I live in, my apartment is usually at least 26 C, I keep my Coconut Oil in the fridge or it would always be a liquid. I'm also extremely new to soap making, having started in November. I have made 6 batches total, which other than some fun with an FO were problem free, but that's not a huge amount of batches, I am by no means an expert, and what I am about to describe is just what works for me so far.
I start by mixing my lye and distilled water. I let that cool for about 20 mins, then melt my hard oils and add them to my liquid oils and get started. I do like to make sure that the lye and oil containers both still feel on the upper side of warm to the touch. By that I mean they are still giving off heat, but not so much that they are uncomfortable to hold. I have read some peole refer to this as baby bottle warm, but I have no experience with baby bottles, so your mileage may vary with that.
I know I am at a disadvantage for troubleshooting if anything does ever go wrong, and when I did a batch that used cream, I actually did check temperature for that one as milk soaps are prone to overheating. I've actually been thinking lately of measuring my temps when I start so that I have that information if something goes wrong.
My point in posting this is that, imo, if your temp is 105 or 100 instead of 110, don't panic. It's not going to ruin your batch. The reason temp can be such a useful tool is if you use a lot of hard oils, such as Palm, Shea Butter, etc, if your temp is too low, the oils can start re-solidifying, which leads to false trace. It's also helpful when working with a milk as your liquid, or anything lse that can cause overheating such as honey, etc as it gives you the information to prevent it from happening. And in general, the cooler your temp, the lomger it will take to trace.
But, again imo, you don't have to "tinker" with temp alot. As Shawnee mentioned, some people soap at room temperature, because that is what their preference is. I know you are probably nervous because of what happened with the first batch you posted about, but I think that is due more to a problematic recipe than anything else.