Don't add ice cubes to a tank, or frozen bottles of water. They melt and cool the water then the water warms up so you add more which cools the water again. In nature the temperature changes slowly from night time cooler to day time warmer; it does not change suddenly from hour to hour. This is bad for fish.
Changing the room temp if you have AC is the way to go.
With a silent cycle, if there are enough plants you should have virtually no increase in nitrate unless you are using a fertiliser containing nitrate. The plants should use all the ammonia so there shouldn't be any left to be turned nitrite and then nitrate.