20 Amp Dedicated line: 10 gauge vs 12 gauge wire

From all that I've read, it's about voltage drop over the distance of the circuit run. At shorter distances from your breaker box (perhaps under 30') go with 12 gauge, at longer distances (50' or more) definitely use 10 gauge. I've seen some charts showing the voltage drop over distance, and it can be significant, but I can't find them now.
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No problem using 10 gauge instead of 12, however if all your outlets are rated at no more than 20amps, you should use a 20amp breaker.

Neither wire will heat up noticably, because you will only draw a couple of amps no matter what the wire, outlets, and breaker are rated for.