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She warmed herself by the fire.
Literal
She [topic-は] fire [at-に] basking [then-て] body [object-を] warmed.
火にあたる is a useful set use of the verb 当たる: 'to be exposed to (heat, light, sun, wind, fire),' i.e. 'to bask in / warm oneself at.' The に here marks the heat source one is exposed to. It's the same あたる as in 風に当たる ('cool off in the breeze') and 日に当たる ('get some sunlight'). After the て-form connector, 体を暖める ('warm one's body') wraps up the action: she sat by the fire and as a result warmed up. A homely, atmospheric scene of pre-modern domestic life.