Sure, I’m happy to help.
Contrary to many beginning soaper instructions, the oils don’t need to be within 10 degrees of the lye solution. That means there is no need to heat the lye solution after it has cooled.
You also don’t want to refrigerate your lye solution. A 50% lye solution will precipitate out (separate) below 65 degrees, and you will end up with a chunk of solidified lye at the bottom of your storage jug.
I use my premade lye solution at whatever room temperature it happens to be (usually 68-80, depending on the time of year).
As for my oils, I start my soaping sessions by measuring them and melting them until just clear. Then I measure and prepare everything else, including colors, scents, additional liquid, additives, tools, mold(s), etc.
When that’s all done, I put on my PPE and weigh out the MB lye solution. By that time, my oils are just warm to the touch, and ready to soap. I don’t typically measure the oil temp, but when I have, it is 90-100 degrees F.