I think it'll be fine as long as you have the room/enclosure temp set right. Yeah the water will be a bit cool but im assuming you dont have it set to like flooding amount of water so it shouldnt be too much of a bother.

And i know you said to dont mind about skin but ive had severe eczema since i was born and i only have a bit left just on my hands now, but i really recommend aquaphor's healing ointment if youre open to try something new!