You know, I will thoroughly admit to NOT letting things sit till at room temp. I have been known to dump them in my sink or bathtub and let them cool a bit (after letting the crockpot sit open and off for a bit first)) before rinsing. I have yet to felt something this way, but if the dyes need time to set it won't work of course.
For production dying, what I do (I'm constrained by space to dry more than anything else): wind skeins one day. Leave them to soak in the tub or giant bucket. Make up a bunch of dyestock if you dye using DOS (I don't, I make it up as I go along).
If I need to dye 10 of one thing, I will suspend them above the pot after thoroughly soaking them. For solids it is more complicated and involves turning the yarn a bunch*, but for multi shades I just lift them and turn as need be above my pots, adding dyes as I go along (start with the lightest). Or, I lay them out in a giant dish/pan to paint the yarns
I find it faster to dye in larger lots and then re skein if you are going to be reskeining- so if you skeins are each 8 ounces, dye them all at once, then skein them again. For roving, if I want the same dyelot as the yarn I will skein it up too and dye it right along with the yarn- I just figure 8 tie it in several places first before soaking.
*I wish I could find a picture of how they do this in Nepal with their dye vats- except there, they connect the skeins together with giant rings, and then turn this handle- something like this though that doesn't show it well. Needless to say, I don't have that equipment in my kitchen.