W biurze działa klimatyzacja, ale w domu wolę włączyć wentylator, kiedy jest gorąco.

Because w means in or at here, and when it expresses location, it normally takes the locative case.

• biuro → w biurze = in the office
• dom → w domu = at home / in the house

So this is not the basic dictionary form of the noun; it is the form required by the preposition w when talking about a place.

These are just the normal locative singular forms of those nouns:

• biuro → biurze
• dom → domu

Polish locative endings are not completely predictable from English, and different nouns can take different endings such as -e, -u, or -ie. So w domu is simply the correct standard form and needs to be learned as part of the noun’s declension.

Działać means to work, to function, or to be operating.

So:

• działa klimatyzacja = the air conditioning is working / running
• jest klimatyzacja = there is air conditioning

That is an important difference:

• jest klimatyzacja talks about existence or presence
• działa klimatyzacja talks about operation

In this sentence, the idea is that the AC is functioning in the office.

Klimatyzacja usually means air conditioning as a system or general cooling setup, not necessarily one specific machine.

If you wanted to talk about an individual unit or device, you might use klimatyzator.

So here:

• klimatyzacja = air conditioning
• klimatyzator = air conditioner / AC unit

Because Polish often drops subject pronouns when the verb ending already shows who is doing the action.

• wolę already means I prefer
• the ending -ę tells you it is 1st person singular

So ja wolę is possible, but ja is usually only added for emphasis, contrast, or clarity.

The dictionary form is woleć = to prefer.

In the sentence:

• wolę = I prefer

This verb is commonly followed by an infinitive:

• wolę włączyć wentylator = I prefer to turn on the fan

So the structure is:

• woleć + infinitive

This is a question of aspect, which is very important in Polish.

• włączyć is perfective
• włączać is imperfective

Here, włączyć is used because it refers to a single completed action: turning the fan on.

So:

• wolę włączyć wentylator = I prefer to switch the fan on

If you used włączać, it would sound more like a repeated or ongoing action, such as I prefer turning the fan on regularly or I prefer to be switching it on, which is less natural here.

It actually is in the accusative case, but for a masculine inanimate noun like wentylator, the accusative singular looks exactly like the nominative singular.

So:

• nominative: wentylator
• accusative: wentylator

That is why the form stays the same.

Because gorąco here is used in an impersonal weather expression:

• jest gorąco = it is hot

This is the normal Polish way to describe weather or general temperature conditions.

By contrast:

• gorący is an adjective meaning hot and must describe a noun
  • gorąca kawa = hot coffee
  • gorący dzień = a hot day

So for weather or how the environment feels, Polish usually uses:

• jest gorąco
• jest zimno
• jest ciepło

Yes. In this sentence, kiedy introduces a time clause:

• kiedy jest gorąco = when it is hot

It tells you under what condition / at what time the speaker prefers to turn on the fan.

Yes, in this sentence gdy would work very well.

• kiedy jest gorąco
• gdy jest gorąco

Both mean when it is hot.

The difference is mostly stylistic:

• kiedy is very common and neutral
• gdy can sound a little more formal or literary

In everyday speech, kiedy is extremely natural.

Because kiedy jest gorąco is a subordinate clause, and in Polish such clauses are normally separated by a comma.

So the comma marks the boundary between:

• the main clause: W biurze działa klimatyzacja, ale w domu wolę włączyć wentylator
• the subordinate clause: kiedy jest gorąco

This is standard Polish punctuation.

Ale means but, and it introduces a contrast.

The contrast is:

• in the office, the air conditioning works
• but at home, I prefer to turn on a fan

So ale connects two different situations and shows opposition between them.

No, Polish word order is fairly flexible, though some versions sound more natural than others.

The original sentence:

• W biurze działa klimatyzacja, ale w domu wolę włączyć wentylator, kiedy jest gorąco.

sounds natural and gives early emphasis to the places:

• in the office
• at home

You could also say:

• Klimatyzacja działa w biurze, ale w domu wolę włączyć wentylator, kiedy jest gorąco.

This is also correct, but the emphasis shifts a little. Polish often moves words around to highlight different parts of the sentence rather than to change the basic meaning.

Yes, and it is a useful one to notice.

• działa comes from działać, an imperfective verb
• włączyć is perfective

Why?

• działa describes an ongoing state: the AC is working / functions
• włączyć describes one complete action: to turn on the fan

So the sentence naturally combines:

• an ongoing situation in the office
• a one-time action the speaker prefers to do at home

That is a very typical Polish use of aspect.