The answer is a solvent. Milady states plainly that synthetic hair solutions should always be cleaned with a solvent, not water alone.
Hot water specifically should be avoided — the book notes it can cause the hair solution to be damaged — which rules out one of the tempting-sounding wrong choices directly. The recommended process is to immerse the piece in lukewarm water with the manufacturer's specified solvent, not to rely on water temperature alone.
Milady Standard Barbering, 6th ed., Ch. 15 (Men's Hair Replacement), p. 505: "Synthetic hair solutions should always be cleaned with a solvent."
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