I would put the fan on lighting circuit and put the heater on the receptacle circuit on LOAD side of the GFCI. That way the heater will have GFCI protection.

No it may not be allowed on the bathroom GFCI circuit. You only have 500 watts load on the new 15 amp circuit so I would add it to the lighting circuit.
Although now that I think about it, if there are not any other bath receptacles on the new #12 circuit it would be OK to add it to that one. I would still add it to the lighting circuit though.

Read the information on the fan/heater. Many specify what sort of circuit and GFCI protection they are to be installed on.

The fan says to use a GFCI if it is over a shower. I can still get the #14 wire GFCI protected by doing it at the breaker panel, if that is OK with having recessed lights on it too? Or should I put the fan and electric mat on the #12 wire of the load side on a GFCI outlet? I guess I am trying to figure out what makes sense from a load perspective. I do not understand enough about the impact of the mat which is rated at 360 watts and 3 amps. But the fan must be basically a neglible load. It seems 360 watts is neglible too? Although there several set up of lights in the bathroom, they really won't all be on at the same time. Am I worrying about nothing, the gutted bathroom was previously feed by one #14 wire in addition to other load outside the bathroom.

360 watts is like 6 - 60 watt light bulbs burning, no? And the #14 circuit has 8 lights X 60watts = 480watts. So the total would be 840 watts. Is this correct? I guess if the total is less than a 1000 watt hair dryer, you are OK??????

Be careful with electric mats. They can overload your wires causing them to melt in the wall and cause fires. Once the insulation melts off, you will have exposed conductors. I heard they are worse than hair dryers.

mowers, do you have anything to back this up? i have never heard of this...

Now I am confused..??? Need help.

Can someone clarify what circuit the fan and electric mat should go onto?

What will melt, the actual #12 or #14 wires? I never heard of this before. Are you saying the actual plastic jacket will melt off and I will have bare copper exposed behind the wall???? How can this happen?

Place the bathroom vent on the lighting circuit. Protect it through a GFCI only if it will be inside the shower area.
Place the heating mat on the receptacle circuit ONLY if that circuit services only that bathroom. The thermostats that are designed to work with the mats have an integral GFCI, so additional GFCI protection is not required.

Normel...thanks for figuring this out. Yes, the #12 outlet circuit only has 2 outlets in the bathroom on it and is dedicated for the just the bathroom.

Can the electric mat be supplied from a GFCI protected wire, or does the supply need to be non-GFCI protected? I was planning on running a jumper from the one outlet which is a regular outlet to the electric mat. This regular outlet is feed from the other GFCI outlet protected lug. Sounds confusing, but can a GFCI wire feed a GFCI electric mat, kind of like 2 GFCIs in a row.

Got the mat today in the mail...the instructions "recommended" a dedicated circuit...is this kind of overkill...why. Are they covering their "butt?"

I personally would just go with a dedicated circuit. If you have in on your bathroom's 20A circuit I'm willing to bet you'll get a lot of nuisance breaker trips when you switch on that 1875 watt hairdryer.

Please pay no attention to what mowers has said. Nothing will melt or catch fire if it's properly installed on an appropriately sized circuit.

I do not have another circuit without doing major work to get one there. Am I better off installing it on the #14 lighting circuit with the exhaust fan and recessed cans (so it is not on the outlet #12 circuit)?

Pete,
You have a 20 amp circuit and a 15 amp circuit that you are working with. Watts = Amps * Volts, so just do the math. Any time you demand more current than the breaker can carry it will trip (20 amp breaker = 2200 watts, 15 amp breaker = 1650 watts). Total up all of your loads (including 1500 watts for a hair dryer) and see which one is going to have the most excess capacity after you add the heat mat. If there isn't any available, then don't use the heat mat. Remember that you can install compact flourescent bulbs and lower you lighting load. If in doubt (which obviously there is some) have it inspected. As a matter of fact you should be having it inspected anyway. Good luck.