Learn Hardcore Finnish: Kun minua paleltaa illalla, juon kuumaa teetä keittiössä. - When I feel cold in the evening, I drink hot tea in the kitchen.

Kun most often means when (time). In this sentence it’s when/whenever: it describes what you do at those times you feel cold in the evening.

Kun minua paleltaa …, juon … = When/Whenever I feel cold …, I drink … If you wanted a clearer if meaning (a condition rather than time), you’d typically use jos.

Why is there a comma after illalla?

Finnish normally uses a comma between a subordinate clause and the main clause:

Kun minua paleltaa illalla, (subordinate clause)
juon kuumaa teetä keittiössä. (main clause)

What is going on with minua—why isn’t it minä or minulla?

With cold/heat-type sensations Finnish often uses an “experiencer” in the partitive:

minua paleltaa = literally something like it chills me / I feel cold So minua is partitive of minä.
A very common alternative structure is:
minulla on kylmä = I am cold (literally I have cold)

Why is the verb paleltaa in 3rd person singular, even though it’s about I?

Because paleltaa here is used in an impersonal/expression-like way: the grammatical “subject” isn’t I. The feeling is expressed with:

experiencer in partitive (minua)
verb in 3rd person singular (paleltaa)

So minua paleltaa behaves like a fixed pattern: “it makes me feel cold.”

What’s the difference between paleltaa and palella?

Both relate to being cold, but they’re used differently.

minua paleltaa: “I feel chilly / it makes me feel cold” (impersonal pattern with partitive experiencer)
minä palelen: “I am cold / I’m freezing” (the person is the subject; verb agrees with them)

Both can be correct; the sentence you have uses the impersonal style.

Does Kun minua paleltaa illalla mean “when I’m cold in the evening” or “when evening makes me cold”?

It means when I feel cold in the evening. Illalla just sets the time (in the evening); it doesn’t act as the cause. If you wanted to emphasize a cause, you’d typically mention it explicitly (for example wind, weather, being outside).

Why is illalla in that form—what case is it?

Illalla is the adessive form of ilta (evening) and is used for time expressions:

aamulla = in the morning
päivällä = during the day
illalla = in the evening
yöllä = at night (a different word)

So illalla is the normal “in the evening” time form.

Why is it juon kuumaa teetä and not something like juon kuuman teen?

Kuumaa teetä is partitive, which is very common when you mean an unspecified amount of an uncountable substance (tea as a mass):

juon kuumaa teetä = I drink (some) hot tea

Kuuman teen (genitive/accusative-like total object) would suggest a more bounded/complete amount, like “I drink the hot tea / I drink a (whole) cup of hot tea,” depending on context. In everyday speech, partitive is the default for beverages.

Why do both words change: kuumaa and teetä?

Adjectives agree with the noun in case and number. Since teetä is partitive singular, the adjective is also partitive singular:

kuuma (basic form)
kuumaa teetä (partitive singular)

What case is keittiössä, and what does it express?

Keittiössä is the inessive case, which means in(side):

keittiö = kitchen
keittiössä = in the kitchen

So it tells the location of drinking the tea.

Is the sentence talking about a habit (whenever) or one specific evening?

Most naturally it reads as a habit/general pattern: Whenever I feel cold in the evening, I drink hot tea in the kitchen.
If you wanted to emphasize one specific occasion, you might add context (like tänä iltana = this evening) or use surrounding sentences to anchor it.

Can the word order be changed?

Yes. Finnish word order is flexible, mainly used to control emphasis.

Kun minua paleltaa illalla, juon kuumaa teetä keittiössä. (sets the condition/time first)
Juon kuumaa teetä keittiössä, kun minua paleltaa illalla. (focuses first on the action, then adds the “when/whenever” clause)

Both are grammatical; the nuance is about what you foreground.