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That just presumes your conclusion: that properties exist just in abstractions.There exists no fire that is not an abstraction of certain set of stimuli. Whatever you think of as "fire" is in this regard indifferent to a mathematical description of how it works. Physical world doesn't have properties, only abstract objects have them. A map and a terrain are both samely abstractions of the same chunk of sensory data, only the second is perhaps more fine.
Even if we accept that fire is an abstraction, it doesn't mean that the abstraction itself is hot.
A map shows a landscape without actually being that landscape../