Left sun radical anchors 暖 as warmth-from-sunshine. In classical thinking, the sun is the primary source of heat, so 日 marks heat words alongside 晴 sunny, 晒 to bask, 暑 summer-heat. The radical sets the thermal frame for the whole character.
Right component 爰 supplies the sound - yuán drifted to nuǎn, a regular Old Chinese alternation. 爰 itself shows two hands passing something between them, which adds a faint warmth-being-handed-over flavor. Same phonetic recurs in 援 to assist and 缓 slow.
