I've played with lots of temps and situations. My first batch, maybe first two - I know it didn't last very long - was the painful process of matching temps. After that I moved on to thermal transfer - using fresh made lye to melt hard oils. I made my lye, measured out each oil, and carefully added each oil to the lye and hand stirring, allowing the hard oils to melt before adding the next oil. (Carefully adding the oils to avoid splashing the lye out of the pot - dangerous! Knowing better now, I recommend putting all the oils in the bowl and adding the lye to that in one go.) That worked well for me for a year and a half, through several different recipes while I was experimenting to find a recipe I loved. When I started selling, I very quickly switched to masterbatching my oils and using fresh lye. Masterbatching oils: I melt 12lbs of oil together and pour into a bucket and let it cool. I remove what I need for each batch. My current recipe is 65% hard oils, and the masterbatched oils have the consistency of a loose balm, slightly looser than vaseline (if I remember vaseline correctly, I haven't touched the stuff in years). This year I moved on to masterbatching lye, so my lye is about 120°F when I add it to my oils. If the soap dungeon is chilly, I might warm up my oils in the microwave for 30-60 seconds to loosen it up a bit, but it's not hot, more like slightly warmish. About the only thing I haven't done is adding room temp lye to completely melted oils... oh, wait... yeah, I did that too with my first beer soap. It worked fine. So all that said... there's a lot of ways to make soap.
One thing that I noticed is that even room temp lye and room temp oils will warm up when combined. I believe this is the "energy" of the saponification process [disclaimer: not a scientist nor do I play one on TV]. I feel that this reaction would override the concern of cold lye making the oils hard. YMMV depending on what/how much hard oils you have. It might not be enough if you had something like stearic acid, or a ton of cocoa butter in the recipe.