Took a bit of time but with today's clue, I think I've got a solution. The carols are spoilered separately at first for anyone who wants to check without seeing my other identifications.
First, we start by converting the Solfege into the carols:
1. Good king Wenceslas
2. Love came down at Christmas
3. We three kings of orient are
4. Our day of joy is here again
5. Hark! The herald angels sing
6. Silent night, Holy night
7. Redeemer of the nations, come
Next, sort them into
Alphabetical order:
- Good king Wenceslas
- Hark! The herald angels sing
- Love came down at Christmas
- Our day of joy is here again
- Redeemer of the nations, come
- Silent night, Holy night
- We three kings of orient are
and extract letters by
Removing punctuation and spacing, and reading diagonally downwards, in keeping with the Professor's name and preferred temperature:
Goodkingwenceslas
hArktheheraldangelssing
loVecamedownatchristmas
ourDayofjoyishereagain
redeEmerofthenationscome
silenTnightholynight
WethreEkingsoforientare
to give us
GAVDETE in Classical Latin
So the 8th carol must be
Gaudete, gaudete! Christus est natusGaudete, gaudete! Christus est natus
which is only appropriate for Gaudete Sunday - credit to @Stiv for the connection