I believe hot weather could contribute to faster set up time because it can help heat up the soap. I have had soap heat up quite a lot more than normal in the heat of summer than it does in the winter when not insulating.
Whereas in the very coldest part of winter, I know that at least one member here has mentioned using the snow (I would probably just use my cold concrete garage floor) to inhibit soap from gelling.
But I am not sure if your question is does the heat make it take longer to firm up? If so, it would depend on if the heat is so high that it keeps the soap too hot. I believe that could happen if it gets as hot enough, but unless you are putting your soap in a spot where the heat is far more than you or your pets can personally stand, probably not.