All depends on the yeast, and it's temp range. Some have a narrower optimal range than others, and can produce off flavors when fermented too warm. For the 1118, which I used (and I believe disturbed chemist did too), it's range is 10-30 C, which is 50-86 F. So, unless your room temp is warmer or colder than this, you should be good to go in the closet! That's where I did mine.
And in response to the other post - I didn't carb mine; just left it still when bottled. But a bit of carbonation might accentuate the taste somewhat... Won't know 'til you try!
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