My baby also sweats a lot, especially when he is dringking milk. When it is getting hotter now, his hands and legs become sticky and cold. I don't know whether it is normal or not. We have turned on the fan when he was sleeping and he seemed to feel comfortable. Without the fan, he cried and refused to sleep.
My baby also sweats a lot, especially when he is drinking milk and sleeping. Last week one of my relatives introduced me to cook 神骨煲北蓍湯(神骨系豬骨一種) for him. I put the soup on the rice to feed him.
The soup is work. My son took just two times of the soup, the sweating situation has improved a lot. That also makes him sleep better than before and not so easy to lost temper. He grasped his head seriously when he is in heavy sweating. He is now not sweat so much and thus seam becomes gentle. You may try, it is easy to cook and also suitable for mum!