There's a difference of perspective. känner sig is about how someone feels in the sense what they experience. How något känns is about how the speaker experiences the thing. So jag känner mig varm 'I feel warm', (I experience this), but Rummet känns varmt 'The room feels warm', the room does not experience this, I do.
I still try to figure out the difference between känner and känns: Is "Hur känner du" how you feel (How do you feel?)? And "Hur känns du?" the feelings you have about feeling yourself? "How does it feel to feel yourself?" Is känner - känns a little bit in the way you use our German word "wahrnehmen"?
Have you read my post about the deponent verbs here: https://www.duolingo.com/comment/6094592 ? It might be helpful.
hur känns du would only refer to someone else's experience of you, so it would be somewhat odd to ask that.
If someone touches you and thinks your skin feels cold, they could say Du känns kall 'You feel cold [to me]', because then they experience that.
But you yourself would just känna dig kall.
I think, now I understand a little bit better: It is in a way like in German "fühlen" and "anfühlen", "ich fühle (etwas)" and "Ich fühle mich ... an".
"Ich fühle mich alt" = "Jag känner mig gammal". "Ich fühle mich alt an" = känns. (You wake up one morning, touch your skin, count the years... It is, even in German, an unusual, more philosophical sentence, but it works.) So "Du känns gammal" is a sentence you better shouldn't say to your girlfriend or wife. I hope, I've got it...