Like i thought and said it didn't do anything to her.
Nami dispersed her snow form with heat but it didn't damage her real body.
Well obviously if you can disperse her snow form by melting it it will delay her and push her back cause she has to regenerate it, that's why Nami says "It works".
You can clearly see in the panel Nami blew up her entire arm with the heat ball yet you can also clearly see that the snow is forming around it like it is only being dispersed.
If it truly affected her real body then her entire arm would've been gone...
Also there are no burn marks on her as well as neither blood nor bruises...
The "kyaa" seems more like a "surprised" reaction not a "being in pain" reaction.
The panel you provided is actual clear evidence that heat did in fact NOT affect her real body at all.
Monet rebuilt/regenerated her arm without problems that wouldn't be possible if actual damage to her real body was caused.
Here she gets cut in half with haki and doesn't regenerate from it, also you can see in that panel that there is no snow forming/dispersing around the cut part because haki bypassed the intangibility.
So in conclusion if the mera mera melts Monet without haki she will just regenerate/rebuild herself in the same fashion, nothing suggests otherwise.
So the same logic also applies to when Akainu and Aokiji hit each other without haki.
The reason why fire can melt ice easier than Magma is because magma is heated liquified rock with a lot of mass whereas fire is heated gas without any mass.
If you try to melt ice with flames it will melt a lot faster than when you put lava on it, in fact depending on the amount of ice putting magma on it doesn't even allow the ice to be melted entirely since the magma will be cooled down at some point.
Experiments from youtube:
Flames vs Ice
Lava vs Ice: (Also keep in mind this is a much more liquified version of it, Akainu's Magma is more solid than this)