I have several IRL soaper friends, and between the 4 of us we all use different methods.
Friend 1 (who taught me how to make soap) Melts her oils together, mixes her lye, covers everything and mixes it all together the next day. I believe this is "true" room temp method. *note, she also does not have children or other people living with her, or naughty cats that get on the counter. Her recipe is +60% liquid oils. When she taught me, she had me bring each temp to 110°F approximately.
Friend 2 soaps at 95°F.
Friend 3 uses heat transfer with fresh lye to melt her coconut oil and adds in her room temp liquid oils. She doesn't use tallow or butters.
I use 'kind of' heat transfer method. I masterbatch all of my oils into big buckets - I use tallow, cocoa butter, shea butter and coconut for hard oils at 65% of my recipe. If my soap lab is really warm, I have to do a lot of mixing as there will be some liquid in the bucket. I do not use my MB oils if it doesn't incorporate back in, or if there are visible solid chunks. I measure out my MB, which is very creamy consistency, and add fresh lye.
I have tried the "true" heat transfer method with other recipes, some of the trick is adding in solid oils one at a time in order of highest melting point first, and using smaller chunks. (For butters I have only tried this with shea, I have not tried it with cocoa butter, or other hard butters.) I think the recipe I used it for was 1:1 hard to liquid, with lard, coconut, and shea for hard oils, and olive and castor for the liquid. These were small batches at 1lb oils, so for larger batches I could imagine the results would vary if I were to try it again at larger amounts.
It is interesting that everyone has different methods, and different results based on recipes, but yet we all end up with soap. I agree with TEG that bringing everything to similar temps is a great way to start out and brings reliable results. It certainly teaches one lessons when one tries other methods.
(For a good laugh, before I found this forum, I thought I invented the heat transfer method because I couldn't find it anywhere in my reading. It occured to me at my third batch that the lye is hot and would melt my oils - at that time I was doing 30/30/30/10 lard, coconut, olive and castor - and I tried it and it turned into soap! I thought I was a genius! A year later I joined here and discovered that it is more common than not...)