Longer term keg aging...How important is temp?

Have a fermentation chamber that only fits 2 buckets, I'd like to free up a bucket and space in the chamber.

I have a breakfast stout thats been fermenting a little over 2 weeks. Ideally, I'd like to transfer to a keg-seat the lid with 30 PSI and age it longer term in my basement that swings a bit in tempeture (57-65) before putting it on tap. Being that fermentation is complete, how important is a constant temp at this point?

I generally stop maintaining temp and bring it up to room after fermentation is done. I have aged my chocolate stout at room temp swings of 60's to 80's for a few months and it just got better and better. I think the biggest thing is sanitation and purging out the oxygen for extended keg aging.

You will be fine holding it that temp. I just wouldn't want it to get too hot.