Only three degrees difference without climate control, you are doing well. I raise mine in the coop and sometimes have temperature swings from below freezing to in the 70's in a day. Especially when you have temperature swings your brooder needs to have a warm enough spot in the coolest temperatures and a cool enough spot in the warmest temperatures. There is no way to keep an entire brooder at a certain temperature with temperature swings. A broody hen does not have a perfect stable temperature to work with. The chicks eat, drink, and play out from under her until they get cold, then they go back under her to warm up. Try to think along those lines.I currently live in a house that does not have AC and ambient temp in the room with the 7 new chicks ranges from about 85 to 82
I use a heat lamp in my 3' x 6' brooder to keep one end toasty but let the other end cool off as it will. Sometimes there is ice in the far end. They mostly stay on the warm end then. If the temperature gets warm they get away from the heat. The warm end can be well over 100 F as long as the far end is cool enough. I find that they can manage that straight from the incubator or post office. You can get the same effect with a heating pad cave or a heat plate. Some heat plates are not rated for below 50 F but in your house you would be OK. Inside your house your target should be to have the far end of the brooder at ambient temperature. That will be cool enough no matter how old they are.
Too much heat is as big a danger as too little. I'd be nervous if they didn't have a spot they could go to that was below 90 F with cooler better, especially as they age. There is no need for the warm spot to be above 90 F as long as it is 90 F in the coolest temperatures. As they age that can drop, but if they have a cooler spot to go to it doesn't matter. They will go where they are comfortable. By having a warm spot and a cool spot you take all the worry out of it.