Hi (I am Italian): even if the correct statement is --"I have got a flu/ a fever", in this case you are expressing a personal point of view since you only know HOW you really feel. This is very common in fact, when helping a doctor making a diagnosis: --- "Can you please describe how/what do you feel?" Basing on English phrases that I see around (especially in Lyrics), I think that "I'm feeling warm" is correct, but I would say it: -- "I feel kind of warm" [--- EDIT => I'm feeling kind of warm ] where its fuzziness puts an emphasis on your personal sensation.