Derating Switches And Conductors In A 3-Gang Switch Box

I am replacing a fan-only unit with a fan-heater unit in my bathroom.
The switch for the existing fan is in a 1-gang box on a 15A, 14g circuit. Next to the fan switch, in a separate 1-gang box is a dimmer for the bathroom light which is on a *different* 15A, 14g circuit. The new fan-heater requires a 20A circuit so I have pulled 12g Romex up into the attic. The existing 15A circuit for the existing fan will be removed.
My plan is to use a 3-gang switch box for the dimmer, humidity sensing switch for the fan and countdown timer for the heater. I want the dimmer to remain on the existing 15A, 14g circuit. Moving it to the 20A circuit would require rewiring of the walls sconces with 12g and a bunch of other work.
I know that I am allowed to have 2 different circuits in the same switch box and i know that I should derate the dimmer, which is not a problem - it's a 600 watt dimmer for two 60 watt bulbs.
However, I'm not sure if I am getting into a situation where I should be derating the conductors to the dimmer, which would mean rewiring that whole circuit. When I do I need to be concerned with derating the conductors that are in a 3-gang switch box?
If it matters, the 3-gang box is 3.5 inches deep, the deepest I could find. It will contain the switched hot wire for the 15A light circuit, the source wire for the 20A circuit, a switch leg for the fan and a switch leg for the heater.
Thanks.
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Not sure what you mean by derating the conductors. I take it that you have # 14 wire and maybe you think you should have something like # 16. You do not do that. YOu can always use larger wire.
I take it the breaker is set up for 15 amps so you have # 14 wire for it. You do not derate the wire going to the dimmer from whatever the breaker is rated. If the breaker is rated 15 amps, then you must use # 14 wire or larger going from the breaker to the dimmer and then to the lights.
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I don't claim to understand all of it, but see here for a discussion on derating conductors.
http://www.southwire.com/support/DeratingAmpacities.htm
One of the requirements related to derating is the number of conductors in a raceway or cable. I'm trying to find out if that impacts what I want to do in the switch for the light/fan/heater.

Yes, I know that. No, I would never go smaller. That is why I mentioned that I will have 12g wire for the 20A circuit in the same switch box as the 14g for the 15A. The question is exactly that. Do I have to go up to 12g for the 15A circuit?

See above.
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On Fri, 14 Mar 2014 23:32:25 +0000 (UTC), DerbyDad03

You don't derate for box fill. If they fit they fit. 2 cu/in for all the 14s, 2.25 for the 20s.(current carrying) Count all the grounds as one 2.5" conductor and 4.5 cu/in for each switch.
The only time you have to derate is for dimmers.
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Thanks. That's what I was hoping to hear.
However, I do have to question your statement about only derating for dimmers. Not arguing, just trying to understand. I understand the need to derate for dimmers because of the heat. What about this site (and others) where they discuss the need to derate the conductors based on temperature and the number of conductors in a raceway/cable?
http://www.southwire.com/support/DeratingAmpacities.htm
The whole issue of the derating of conductors is confusing to me, although as far as I can tell, I'll probably never have to deal with it.
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