Kind-heartedly means you do something in a kind and generous way. You offer, forgive, or share, and the manner itself shows a warm heart. Though actually, native speakers do not use this word very often. It is correct, and you will meet it in careful writing, but in speech people more often say kindly, generously, or 'in a kind-hearted way'. When it does appear, it still carries real warmth, not just polite form. It can sound a little heavy because it is long.