Когда я пил какао из термоса, мне наконец стало теплее.

Because Когда я пил какао из термоса is a subordinate time clause introduced by когда = when. In Russian, subordinate clauses are normally separated from the main clause by a comma.

So the sentence is divided like this:

• Когда я пил какао из термоса = When I was drinking cocoa from a thermos
• мне наконец стало теплее = I finally got warmer / it finally became warmer for me

Even if the когда-clause comes first, you still use the comma.

Пил is the past tense of the imperfective verb пить = to drink. It focuses on the process or ongoing action: was drinking / drank.

Here that makes sense because the clause means while I was drinking cocoa from the thermos or when I was drinking cocoa from the thermos.

If you used выпил, that would be perfective and would usually mean drank up / finished drinking. That would shift the meaning toward a completed action:

• Когда я пил какао... = while I was drinking cocoa...
• Когда я выпил какао... = when I finished the cocoa...

So пил is the natural choice if the warming happened during the drinking process.

Russian often uses an impersonal construction for physical sensations and states.

• мне is dative: to me / for me
• стало теплее literally means it became warmer

So мне стало теплее is literally something like it became warmer for me, which in natural English is I got warmer or I felt warmer.

Using я стал теплее would sound odd in this context. It suggests I became warmer in a more literal or unusual way, and it is not how Russian normally talks about temperature sensations.

Similar patterns:

• мне холодно = I am cold
• мне стало холодно = I got cold
• мне лучше = I feel better
• мне стало лучше = I started feeling better

Стало is the neuter past form of стать in an impersonal construction, and теплее is the comparative of тёплый = warm.

So:

• тепло = warm
• теплее = warmer
• стало теплее = became warmer

In this sentence, it means the speaker felt warmer than before.

A very literal breakdown is:

• мне = to me
• стало = it became
• теплее = warmer

So the whole phrase is it became warmer for me.

Because the sentence expresses a change: the speaker was cold, and then they became warmer than before.

That is why Russian uses the comparative теплее = warmer, not just warm.

Compare:

• мне тепло = I am warm
• мне стало тепло = I became warm / I started to feel warm
• мне стало теплее = I got warmer

Тёплым would not fit here. That form is the instrumental singular adjective and would be used in different constructions, for example after стать with a noun/adjective describing what something became:

• чай стал тёплым = the tea became warm

But for a person's physical sensation, Russian normally uses the impersonal pattern:

• мне стало тепло
• мне стало теплее

Какао is one of those Russian nouns that is normally indeclinable, meaning it does not change its form across cases.

So you get:

• я пью какао = I drink cocoa
• у меня нет какао = I have no cocoa
• я доволен какао = I am pleased with the cocoa

The form stays какао.

It is typically treated as neuter in agreement when needed, for example:

• горячее какао = hot cocoa

Because the preposition из = from / out of requires the genitive case.

The noun термос changes in the genitive singular to термоса.

So:

• термос = thermos
• из термоса = from the thermos / out of the thermos

This is very common:

• из дома = out of the house
• из чашки = out of the cup
• из бутылки = out of the bottle

In practice, it goes with the whole idea of drinking: I was drinking cocoa from a thermos.

Russian often allows this kind of phrase without needing to spell out every link. A more expanded version could be:

• Когда я пил какао, налитое из термоса...
• Когда я пил какао из термоса...

The second version is simpler and natural.

A native speaker understands that the cocoa came from the thermos, or that the speaker was drinking it out of the thermos. The phrase works naturally with the whole situation, not just one word in a rigid way.

Наконец means finally / at last.

It shows that the speaker had been waiting for this change for some time. So the idea is not just I got warmer, but I finally got warmer.

That gives the sentence a small emotional nuance: relief, delay, or completion after discomfort.

Compare:

• мне стало теплее = I got warmer
• мне наконец стало теплее = I finally got warmer

Yes. Russian word order is flexible, though different orders change emphasis.

The original sentence is natural:

• Когда я пил какао из термоса, мне наконец стало теплее.

You could also say:

• Мне наконец стало теплее, когда я пил какао из термоса.

This puts the main result first and the time clause second.

You could even move наконец for emphasis:

• Когда я пил какао из термоса, наконец мне стало теплее.

But that sounds a bit more marked. The original version is the smoothest and most neutral.

Usually when I was drinking is the better match here, because пил is imperfective and suggests an ongoing action.

So the sense is:

• When I was drinking cocoa from the thermos, I finally got warmer

In some contexts, English when I drank can also work, but it is less precise about the ongoing nature of the action.

If Russian wanted to stress completion, it would more likely use выпил:

• Когда я выпил какао... = when I finished the cocoa...

In theory, теплее can sometimes be used figuratively, but in this sentence the context strongly suggests physical warmth.

Why?

• какао is a hot drink
• из термоса suggests keeping it warm
• мне стало теплее is a very common way to talk about body temperature or comfort

So a native speaker would normally understand this as I felt physically warmer.

Both can be translated as I warmed up while drinking cocoa from the thermos, but they are not identical.

• мне стало теплее = I felt warmer / it became warmer for me
  This focuses on the sensation or change in comfort.
• я согрелся = I warmed up
  This focuses more directly on the result of becoming warm.

So мне стало теплее is a bit softer and more experiential, while я согрелся is more straightforward and result-oriented.

The original sentence sounds very natural if the speaker is describing how they felt.