Always higher.

What if she starts with ice in the pot but the incantation still says "water"? (She debates with herself for a while before doing this one, and has the "if you're reading this I died doing magic" letter out on the table again.)

Absolutely nothing happens.

Phew. If she swaps out the ice for water and tries again, is the diagram still good or did the failure use it up?

The failure used it up.

How bothersome.

She's going through a lot of diagrams and diagramming time with all this science, and even with the "wait 48 hours and double-check your copying" rule she's going to mess one up eventually. It's worth investing some more time in finding a way to mass-produce them.

Photocopying didn't work, but something more manual might. What if she gets some air-dry modeling clay and an exacto knife and makes some really careful models of all the runes in reverse, arranged mirror-style on a sheet, then paints it with ink and stamps it onto a page? This might take a lot of tries to get first a stencil, and then a painting-and-stamping attempt, perfect enough that she deems it worthy of incanting at.

Once she tries a stamped diagram, that works fine.

Sure, but can she then paint and stamp again with the same stamp until she gets another good one and use that?

Yes, subsequent stamps also work!

Woohoo! No more copying that one anymore, not that it isn't already burned into her brain. More to the point, any future diagrams only need to be done perfectly once. 

Next step: swap out the number in the incantation from "sixty" to "eighty". Holding all else constant, does this produce consistently or intermittently hotter water?

It never goes below eighty and the variance is less, but it varies a bit along the same dimensions.

This magic system demands a lot of precision going in for a relatively noisy result coming out. Maybe controlling for environmental circumstances really carefully will be instructive. Does playing back a recording of an incantation work like reciting it?

Nope. Does nothing and doesn't use up the inscription.

How about reciting the incantation loudly vs quietly? (This was such a good pick for first spell; it has a really easily measurable effect size!)

Volume makes no difference alone, but if she actually whispers, unvoicing all the voiced sounds, then it doesn't work (whether this uses up the inscription depends on whether she started any properly pronounced words before switching to whispering: if she whispers it all, the inscription is still usable, and if she whispers only some, the inscription is used up but nothing happens).

She never tries whispering only some; too much risk that it counts as "stumbling over the incantation". Whispering the whole thing is kind of scary, even.

Too many nights in her room doing science is going to drive her crazy; she goes to the Avalon again for longer than it takes to renew her books and looks through the history section again. Is anyone else browsing today?

There's an older centaur fellow looking at the art history selection and a fullformed nixie lady talking to the librarian about getting an interlibrary loan.

Interlibrary loan, huh? That's an idea. But she hasn't gone through the whole nonhumans section here yet. What's in there today? She vaguely recalls a book on Perytons . . .

The book on perytons is still there. There are books on totem animals, a book of speculation about unicorns, books about the sphinx/dragon war, a book about jackalopes, one book about the Loch Ness Monster, books about angels, books about centaurs...

She definitely wants one on the sphinx/dragon war, but not more than one because she doesn't want to associate herself with the concept of dragons in anybody's mind. She'll get whichever of those looks most comprehensive, plus the most comprehensive one on angels and the one about the Loch Ness monster.

Then she can check out The Extinction War and Angelarium; What We Know And What We Don't and Nessie.

Time to go read Nessie on a bench somewhere and get some, if not fresh outside air, at least fresher air than she's been getting. What do actual secret nonhumans have to say about the possibility of one chilling in a lake in Scotland?

There is a Nessie! She's not a species - one-off creatures just exist sometimes. She's an animal, not a person. One-off animals tend to be magical and to have ways of preventing casual observation by humans, but to turned critters Nessie is sometimes friendly. She likes popcorn.

That makes more sense than a person doing it, except for how "one-off species" is almost a weirder concept than magic. What about angels, that sounds potentially pretty weird too. Do they in fact have six wings and enough eyes for the whole class?

Angels are pretty mysterious but do have a lot of wings, "six" being a possible number. They do not generally appear with extra eyes. They don't talk about where they came from, but they are understood not to have "free will" and to instead be bound to carry out tasks, mostly keeping demons in check. They are supposedly incapable of hurting people who don't "deserve it" so a safe way to get un-possessed is to have an angel stab you: you'll be fine and the demon won't. They are genderless, they can glow, bugbears can't sense them, they live a very very long time though they might not be outright immortal, they're eccentric and rare and asocial and sexless and imperceptible by bugbear senses.