98:29 We may not light an oven on yom tov in order to heat up the house unless the cold is so great that the food is getting cold. If that’s the case, then it may be done for the sake of the food. However, if the cold is not that great, it is prohibited, though one may have a non-Jew do it. (Some say the reason that it’s prohibited is because some finicky people might do so unnecessarily but that the practice is to act leniently in the matter – Rema 511:1. See also Mishnah Brurah 511:4.)
98:30 We are permitted to heat water on yom tov in order to wash our hands(, feet and face – MB 511:9) but not for the whole body. If one needs to bathe an infant, he may not heat water for this purpose even through a non-Jew but he may heat a large volume of water for himself and use the surplus. For example, when one needs a little water for cooking, he may heat even a large pot. He should just be sure to put all the water in the pot before putting it on the fire, adding nothing afterwards. If the child is slightly ill, we may heat water for him through a non-Jew.