Baby sweats profusely in the heat at certain times of the day, is that ok?

Maybe. Sweating is produced by activity of the sympathetic branch of the autonomic (automatic) nervous system and responds to ambient (environment) temperature. Make sure that you are not covering the baby up too much with clothing, blankets etc. If this is not the problem it could be something as simple as sugar in the diet, even if that does sound strange to you!