Is "a fair sweat" modifying "wored up" as an adverb phrase?

"despite the cold, George had already worked up a fair sweat"

I just came across this sentence by googling the definition of "work up", but I'm not sure whether "a fair sweat" is used as an adverb phrase modifying the verb "worked up" or used as an direct object of the verb "worked up". Could you tell me what "a fair sweat" is grammatically modifying in the sentence?