You are right, the designer of that spell got his options all tangled. And his math is off, too.
The spell work as an InIg, in fact it already exist, that's the Vision of Heat's Light spell in AM5, p.141, using as you said a Base 2 and a Vision Target. Or it could work as a MuIm in a way similar to Glowing Footprints of the Thief, which is presented just before it: Base 2, Vision Range, and an appropriate Target, which would allow anyone to see the transformed species and thus the heat. But no way can you use a Vision target with a Muto spell, even if you target the species
The point of the synaesthetic spells is to push out the things you can do with imaginem. Yes: you can do the same effect easier with InIg. That's not the point. The point is that if you are a Jerbiton illusioniust, you can do something similar, even though it is a higher level, using the Arts in which you are strong. It's also to highlight to players that species are in some ways like elemental matter, and get them within the game's cosmology, by demonstrating that you can flip the types of species about.
I'm away from my books until the end of the week, so I can't recheck the numbers for you until sometime next weekend. I think the basic point thought is you are assuming that the species spells do things the most efficient way: they don't and are not meant to, in some cases. They work from the assumption that you have a really high Im score and want to do tricky things with it.
Well, I'll check this when I'm back with my books, but as to the last point, that there's no way to use a Vision target with a Muto spell? I seem to recall there's a specific example in the core rules section on magical senses which has a Muto Mentem spell with a Vision target and an Intelligo requisite, so I think that the statement that there's no way for Muto spells have vision targets is false.