This site talks a whole lot about storing and turning eggs. I'm recommending it to you as much for the turning as the temperatures, but it discusses both.
http://gallus.tamu.edu/Extension publications/b6092.pdf
Most people do great storing at room temperature. I agree with the others about storing them in a cooler part of your house, but people were storing eggs for incubation for centuries before refrigeration was popular.
Growing up, Mom would store the eggs for eating under the sink. When we needed eggs for a broody, I'd get about a dozen from the bucket, mark them, and put them under the broody. We usually had good hatches. We did not have air conditioning and it sometimes got warm in the house, especially in the kitchen when she was canning or making jelly.
If you don't yet have a broody but want to be ready in case one goes broody and you have a limited number of laying hens, you can set up a system where you put fresh eggs in every day and take the oldest eggs out for your personal use every day. You can mark the date on the eggs, have separate cartons for a daily rotation, or have two cartons lined up and put fresh eggs in on the right and take the old ones out from the left. Always have ten or twelve ready to go. Whatever works for you. The reason I'd do this is that a broody usually lays every day just before she goes broody, then quits laying. If I have a hen go broody, I want her to raise some of her own chicks, not as a reward but to keep the broody trait in my flock. You also don't have to turn them if you keep the eggs for less than a week. Simpler is always best.
