I would say it wouldn't make any difference, but why don't you try keeping some in a shed,or other cool place to bottle condition and see if you notice any difference, always better to go off your own experience. As with a lot of topics in brewing there are different opinions which could be debated till the cows come home.
As for Bowl sprayer yes what you are doing is right, once your beer has carbonated leave it in a cold-cool place for as long as you can, you will often hear stories of beer having an off taste and after a good length of time the beer will come good, I had this happen to me with a stout it fermented a bit to high a temperature and didn't taste so good, found the bottles at the back of the shed over a year later and they were fine.