I live on Kauai and like most long-term residents, we do not have central air conditioning. We have A/C window units framed into the house on two bedrooms, but not the child's room.
On a normal summer day in the afternoon, it will be 92 in the living room and 86 in the bedrooms. During this time, we do not turn on the A/C units. We just hang out on our covered porch with breeze. It's normally 82-84 outside. If there is no breeze, we go to the beach, which is an 8 minute drive.
If it ever goes above 86 in our child's bedroom and our 2 year old soon needs a nap, we will put him in our bedroom with the A/C and turn it on for his nap. We can position the pack and play so the cold air from the A/C blows directly over him. It probably doesn't lower the temperature of the room, but it's much cooler for our son while he sleeps.