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legally you can use #10 awg wire but I would recommend using #8 awg wire. It would not get as hot as # 10 awg and could carry any overload you could have before the breaker would trip out...The breaker would trip very fast on any overload or shorted circuit before the amperage could affect either size wire but the #8 wire would just stay cooler. #10 AWG can only be fused at 30 amps per the "note" in national electric code (NEC) even though chart shows its ampacity is greater. Therefore, a load of 38 needs the larger wire. In addition if the furnance contains a motor load (usually it does) the motor part must have an extra 25% capacity added to the wire ampacity. So your 38 amp load may actually need wire sized to 40+ amps depending on the motor load. In addition if the ambient temperature of the room is high (like a boiler room) an additional factor probably need to be added. Refer to the charts in NEC

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Q: What size wire is needed for furnace pulling 38 amps?
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