The mother rabbit is keeping her babies warm with her body.
Literal
Mother-rabbit [topic-は], babies [obj-を] own [gen-の] body [with-で] is-keeping-warm.
暖かくする is a causative-adjective construction: [い-adj stem]+く+する = 'make X [adjective].' 暖かい → 暖かくする ('make warm'). The parallel pattern for な-adjectives is ~にする. 自分 ('self, own') is the reflexive pronoun — here referring back to the mother rabbit. で marks the body as the instrument of warming.