Reduce the temperature of the AC more so as to make the room cooler.. There's no need reducing your child's activity.. They need it. If you are still bothered about the sweat, visit a paediatrician to confirm if its a case of true hyperhidrosis.

The case of excessive sweat (hyperhidrosis) is not so common but it does exist. So I'll say relax, dress your child light, singlets and sleeveless bodysuit should be the wears for this weather. Keep your child hydrated, give alot of fluid preferably water..