All my soaps are milk soaps, and though I have only been soaping since September, I think I can already say that the temperature of your lye and oils depends on what oils you are using. I started off with a high percentage of olive oil plus a bit of coconut and palm, and soaping at room temperature was just fine. When I changed my recipe because I still found it slimy and drying, I upped the palm oil content and added a bit of castor. Suddenly room temperature didn't work for me any more. The cool lye was re-solidifying the palm oil as soon as it hit it.
I don't claim to have the answers because my results are still very hit and miss. Just wanted to say that any small change in any variable can produce a dramatically different result. Good luck! I love my milk soaps and have no desire currently to make soap with water!