This is why I've gone over to using the canned starter wort. No more issues with chilling down the cooked starter wort made from DME before pitching the yeast in. Besides, I'm not really setup where I'm living now to chill a cooked starter wort before pitching the yeast.
As mentioned already, the temperature the starter ferments at isn't as important as the beer the resulting yeast will go into. I don't do any temperature control of my starter as it's spinning on the stirplate. I've seen it get into the high 70's and low 80's before. Cold crash for 24-48 hours (longer if possible) and decant as much of the spent starter as possible.
I'd suggest looking into getting some canned starter (the cans are concentrate, so you add water to those) for the next starter you want to make. You are locked into 1L increments with this. I have yet to really have any issue with that though. I often do two starter steps, unless I've gotten lucky and managed to get to the LHBS close enough to brew day and the yeast they have on hand is fresh enough to only need a single step. With all the insanity in the world right now, I don't go as often as I otherwise would. If we have brew dates set a couple of months into the future, I'll often pick up the yeast packs for those batches.