I decanted the old starter beer and left just a little above the yeast cake. Do I have to get that down to room temperature before adding the new cooled wort?
Not quite sure I understand your question, is your starter at fridge temp? I assume you were coldcrashing if you decanted. You can add the wort as soon as it is cool regardless of yeast temp if you are going to decant anyways in the end. No need to worry about off flavours if you decant.
I'm a little unsure what you're asking, but its usually best to keep temperature changes as small and slow as possible. Yeast tend to like that. Keep that in mind when you brew!