After he realized you didn't turn into ice when he carried you,he realizes that you're his destined one,who will accompany him forever. Kiyomu is a yukiotoko,a snow yōkai.Whatever he touched,someone or something,it'll turn into ice. He took you to his cave and tried to make a fire for you to feel warm,even though his weakness is fire.He can't be under the sun.Heat will make him weaker. Kiyomu is very cold and ignorant to others,but somehow,he is not that bad towards you,his destined one.