。
She gave them a warm welcome.
Literal
She [topic-は] them [object-を] warmly welcomed.
暖かく is the adverbial form of the i-adjective 暖かい ('warm'), modifying the verb. Note the metaphorical use: 暖かい literally describes physical warmth, but here describes the manner of welcoming — friendly, cordial. English happens to share this metaphor (a 'warm' welcome), making the literal translation feel natural even when the structure is being followed strictly.