How do I get a harsh vocal to sound warmer?

There will only be so much you can do. Having said that, you'll want to use either a compressor and EQ combo, or a dynamic EQ to control the frequencies in her voice when she starts to sound brassy. The first time you do this it will take you some time to wrap your head around how this works. Search youtube for some examples.
 
Regards,
Dan

You could take a look at Antares Aspire EVO: https://www.antarestech.com/product/aspire-evo/
 
This has a function to increase or reduce rasp / breath etc.
 
Use the VST2 version of this though - the VST3 doesn't work well with CbB or Sonar.

Try the Pro-Channel "Style Dial Effects" they come with the program and they have many options for making a vocal track much warmer. Start with the "Smoother" effect that warms up the vocal sounds and removes sibilance and harsh frequencies. That is a gem for vocals, sorta like a De Esser.

mettelus
I would suggest Melda's MCharacter, which is the only thing I know of to surgically modify harmonics in real time. 

That's really impressive. I watched the demo video all the way through. I think this will be the closest thing to a magic fix for OP's issue.

The first thing to do is to notch out the "honk" frequencies. Every mix engineer should know how to this. The EQ built into the ProChannel is a great tool for this.
 
I usually make my notches about -3dB.
 
From a Sound On Sound article:
 
"The standard technique for identifying the offending frequency range is simply to set up a narrow-band EQ boost and sweep it across the frequencies until you find the spot where the nasal 'honk' is most pronounced. You can then place an EQ cut at this frequency, which is likely to be in the 800Hz to 1.5kHz range. Once you've found the right frequency, increase the Q to narrow the cut band until the honk just starts to come back, then reduce the Q slightly again so that you're making an EQ cut that's no wider than is really needed to get the job done. It's also a good idea not to use more cut depth than you actually need, as too much EQ is nearly always detrimental to the sound."
 
Next thing after that is to put a compressor on the track set to a 4:1 ratio, about 8-10 mS attack, 100mS release, set the threshold so that the overall gain reduction is about 3dB, set the makeup accordingly.
 
If you do both of those things and your vocal track still sounds harsh, then you can start with the fancier and more drastic efforts suggested above. Basic honk notching should be done for every vocal track, IMO, before any other processing. It really lets me crank a lead vocal up without it sounding obnoxious or stomping all over the other instruments.

revince 1 - not trying to be funny or offensive.  I have someone who can re-sing it for you with that Roberta Flack smoothness.
 
Just another option...

I use the CA-2A levelling amp in the pro channel a lot, but I've found it very useful in the vocal chain just for removing harshness. In compress mode, pan the r32 pot all the way over to HF, and back off the default gain and peak reduction settings until your just catching the peaks. You will hear the difference if you pan the r32 pot around, but I find it opens up the bottoms a little and drops the high mids equally. Then I will attack it with EQ to find remaining offending frequencies and reduce them further. If it is still a problem, I would try a multiband compressor. Craig Anderton did an excellent article once on using multibands to split a track into multi tracks, treating each track with one band of the multiband compressor, then re-mixing each track back to a summed track. This way you could treat the track with most offending issues separately to the rest of the vocal. Lot of work, but if you don't have the luxury to re-do the vocals, this is a good option. Manny Marroquin also has a rather unique plug called the Triple D which has been very useful for difficult vocals. It's a simple, but effective approach.
 
There you go. Too many options   all the best.