Help. Baby's head sweats a lot

From birth, his head would sweat n soak the sheets. But it was so hot as we had a heat wave. But now at 4.months, he still sweats to soaking wet. He sweats when he cries, he sweats when breast feeding especially between my arm and his head and forehead, he sweats when he sleeps. And it is getting cold so he starts sneezing and showing signs of a cold. I wasn't using the heater in his bedroom because I thought he is too hot. And he would wake up sneezing and blocked nose. So I decided to turn the heater on a bit so he ain't too cold and now he was sweating and sneezing so much he would chock on it. So. Change his whole bed and sleeping sack at night since it is kinda wet so he doesn't catch a cold. Meanwhile his hands are cold. So he can't be that hot, can he? I use STH to relieve him of the mucus but more keeps coming as the bad of his head is always wet.