How to protect wire from excessive heat?
You will have to rewire the circuit with a cable rated at 90&deg;C -- type CL2 cables not further marked are only good up to 60&deg;C, as per note 15 to the tables in the UL Wire/Cable app guide.

As to wire gauge -- 18AWG 90&deg;C wire is rated for an ampacity of 14A by the NEC (table 310.15(B)(16)), and the maximum derate factor required for the OP's operating conditions (max 82&deg;C) is .29 from table 310.15(B)(2)(a) -- this means you can only push 4.06A through the cable without exceeding the insulation temperature ratings or upsizing it.  14AWG should be more than ample, even at such a harsh derate -- 14AWG 90&degC; wire can handle a whopping 25A, and since you are derating, you don't have to worry about the terminations being limited to 75&deg;C.  A 14AWG 90&deg;C cable (even with the extra derate being imposed by the limitation to 60&deg;C ampacities in the table by the use of NM or UF) can handle that same 4A with ease, and a 12AWG wire gets you 5.8A