If you do the calcs, you'll find that 10K throws off only 1.44 watts of heat when it sees a full 120 VAC RMS. This does not seem to be much power at all.

Don't let that make you think it won't get plenty hot, though. We're really not familiar with how much heat that can be, especially if it's in a confined space. I've burned my finger on a 1/2 watt resistor that's got 1/4 watt of power going through it. You will definitely need to provide heat sinking for that resistor and the system will have to be comfortable with a small hot spot in it.