Both are grammatically correct. However, both sound odd. Both could be misinterpreted. More natural ways to say this are "The water feels warm" or "The water feels warm to me." "To me" emphasizes the possibility that someone else might have a different opinion. Person A: "The water feels cold." Person B: "Well, maybe it feels cold to you, but it feels warm to me" "I feel that" and "I'm feeling that" are usually used to describe emotional feelings, not physical feelings. For example, "The waves look dangerous, I feel that this might be a bad day to swim."

If you are using 'feel' to mean 'think', the first one is better. If you 'feel' means to touch/ physically feel something (not thoughts or emotions), then I guess the second sentence works better grammatically if the person is in the process of touching the water. That said, I agree with Worldlearner that both sentences seem uncommon.

Both are correct. However, we usually just simply say 'the water is warm' and I don't think I've ever heard anyone anything more complicated than that.

*say anything more complicated