the CL3 rating directly concerns how the outer sheath of the wire bundle reacts to heat. The National Electric Code requires the CL3 rating so that if the wire overheats or the cable is exposed to heat, the sheath will not give off large amounts of toxic smoke.
If you have to skimp on the CL3 wire, don't do it on the end near the fireplace. But, it would be far better to make a trip and buy 10' of the proper CL3 wire.
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