I could add even more to the confusion: GL on the one hand has Clui 'properly the juices and the fruit of Noon, but used for "Sun", Aur, and for sunny warmth' and on the other hand gwâs 'juice' with the Qenya cognate vasa.
I could understand how 'juice of Laurelin's fruit' could be used for the sun's rays and heat, but clui seems to derive from the concept of 'warm(th)' directly (see cluim, cluimri)...

And none of it is related to 'consume' - which I think is meant along the lines of 'singe, scorch, burn/dry up' in this context.. There are certainly plenty of roots related to warmth, hotness and burning in the Lexicons, so perhaps Tolkien decided to make one up on the fly (or reinterpret vasa) without noting it down separately?

Thanks Roman. I think you're right about 'singe, scorch, burn/dry up' in this sense.
One possibility might be if √mbas "bake" had a related root √bas "burn (through), consume," but that's entirely speculation.

Tolkien did indeed like reusing old forms but reinterpreting their meaning; for example he had words related to "cold, chill, winter" from √DYEL, producing Gn. words in Gel-, Del-, etc. But later in the 20s he re-appropriated the root to make Delimorgoth > Delu-morgoth, retaining the derivation but changing the root's meaning to "terrible" (compare it in Etym.)

Like you said, perhaps Tolkien carried over that old word but changed its meaning.

It has been suggested that it could be derived from the √(g)wath root: the stars are 'dimmed' by the brightness of the Sun, it 'consumes' them.

I find both ideas really interesting, but there doesn't seem to be anything resembling later √(g)wath in the Lexicons..
Regarding *√bas, in the Pater Noster Sindarin translation Tolkien actually starts with i v before changing it to i mbas. Probably just a slip, but so might be Vasa.

Hmm, those are interesting solutions. As for √wath, it's found in VT42:9-10 as √wath, √wathar (late '60s) in discussion of Gwathló and Gwathir, as well as Gwathuirim, and √WATH earlier in 30s Etym. - and perhaps in Nebrachar's avosaith (according to Fauskanger's analysis).

My next irritation regards Cermië / Cerveth "July" - I'm not sure about its derivation or meaning. Is it from √KER (meaning what?) and containing -mie (PE17:68) and related -veth, or is the root a  talat or kalta stem like √KEREM or √KERÉM, with the commonly-found -ie and -eth?

If the latter, I have no clue what the intended meaning could be. The former ?might? have some connection with √KWER "revolve" and √KYER "pray, *turn to God," but I'm not sure how such a meaning could be connected to the month of July.

Comparing the Sindarin and Quenya forms, it should be something like *√KEREM- (with an unattested meaning) rather than a compound.

One may get an idea what it could mean from the sequence of month names, freely translated as:
new warmth/sun - wet - windy - sprouting - blossoming - warm/sunny - ??? - hot - harvest - fading warmth/sun - misty - cold
There is really no word between 'warm' and 'hot', so one can eliminate a reference to temperature, I think. My deep gut feeling is that it means something like 'ripening' or 'time of fruits'.
In natural languages, months are often named after a particular plant which blossoms during that time or is harvested, or an animal which comes out; but the Elvish nomenclature seems to be rather generic. I don't have the sources at hand right now, but one should also cross-check with the early names in PM.

A connection with 'revolve, turn' may be that the sun 'turns away' after the solstice; unfortunately √KWER- doesn't quite fit phonologically..

Right - my suggestion wasn't that they could be from √KWER, but rather from an unattested root *√KER that is connected with √KYER and √KWER, i.e. the Interconnexion of Bases in PE18, cp. √KEL / √KYEL / √KWEL. And who knows how the meaning would change from *√KER to *√KEREM ...

"√ kere (kuere, kiere) 'turn'" is attested in Early Qenya Phonology (in PE 14 it is found on p.65).

I'm just back from Omentielva Enquea where Betrand gave an interesting talk on the month names. Apparently Tolkien has largely adapted them from the French Republican Calendar (https://en.wikipedia.org/wiki/French_Republican_Calendar). Cermie would correspond to Messidor, related to 'harvest', so *KEREM- might be somehow related to KIR-, meaning 'cutting, reaping'.
In any case, you can look forward to a very thorough analysis and comparison with natural languages in Arda Philology 6!

+Roman Rausch, I look forward to reading that upcoming analysis! Like those from previous years, the presentations and seminars listed on the Omentielva website's programme look highly interesting. Since the next one will be in California, I may finally be able to afford the airfare, though participants will be different.

Incidentally, I also discovered a few hours ago that Jim Allan came to the same conclusion about the French Republican Calendar back in his 1978 Introduction to Elvish, which I don't have a copy of. I'll have to get one - I'll enjoy reading both of their differing analyses, especially now that we know more about Tolkien's languages than was the case back then.