Learn Hardcore Norwegian: Viften gjør rommet kjøligere, men varmeovnen varmer stuen. - The fan makes the room cooler, but the heater warms the living room.

Masculine: en vifte → viften (definite singular) → vifter (plural) → viftene (definite plural).
Feminine: ei vifte → vifta → vifter → viftene. Pick one gender and stay consistent within a text. The sentence uses the masculine pattern (Viften).

What’s the difference between rommet and stuen? Are they synonyms?

They’re not synonyms.

rom = a room (any room); neuter. Indefinite: et rom; definite: rommet.
stue = the living room/lounge; common gender. Indefinite: en/ei stue; definite: stuen/stua. So the sentence talks about “the room” in general in the first clause, and specifically “the living room” in the second. If you mean the same space, use the same noun in both places.

How does the structure gjør rommet kjøligere work?

This is the causative “make + object + adjective” pattern:

gjøre + object + (adjective/comparative) = “make [object] [adjective]”. Here, Viften (subject) gjør (verb) rommet (object) kjøligere (object complement). Other examples:
Kaffen gjør meg våken. (Coffee makes me awake.)
Malingen gjør veggen lysere. (The paint makes the wall lighter.) You could also say: Viften gjør at rommet blir kjøligere, but the given sentence is more concise.

Why use kjøligere and not kaldere?

kjølig = cool/chilly (mild). Comparative: kjøligere.
kald = cold. Comparative: kaldere. A fan tends to make a place feel cooler rather than truly cold, so kjøligere fits better here. If the temperature actually drops a lot, you might use kaldere.

Could I say Viften kjøler (ned) rommet instead?

Yes:

å kjøle (ned) = to cool (down), which suggests an active cooling process.
å gjøre … kjøligere = to make … cooler (focus on the resulting state/feeling). Because a fan usually improves airflow and makes you feel cooler (without much change in air temperature), gjør … kjøligere is very natural. kjøler ned is also common in everyday speech.

Is varmer transitive? Do I need opp (as in varmer opp)?

å varme is transitive: Varmeovnen varmer stuen (The heater warms the living room).
å varme opp emphasizes the process of heating up from a lower temperature: Varmeovnen varmer opp stuen. Both are correct here; varmer is slightly more general, varmer opp highlights the change.

What exactly does varmeovnen mean? Could I just say ovnen or radiatoren?

varmeovn = a heater (general term for a device that provides heat). Definite: varmeovnen.
ovn = oven/stove; can mean a kitchen oven or a wood stove; ambiguous.
radiator = radiator (usually hot-water or electric oil-filled).
Very common modern heater: panelovn (definite: panelovnen). Use varmeovnen if you want to be clear it’s a room heater, not a cooking oven.

Why is there a comma before men?

Norwegian puts a comma before coordinating conjunctions like men (but) when they link two main clauses. So: Viften gjør …, men varmeovnen varmer …. After men, use normal main-clause word order (subject–verb–object), as in the sentence.

Anything to know about word order and inversion here?

Both clauses have verb-second (V2) order:

Viften (subject) gjør (verb) …
men varmeovnen (subject) varmer (verb) … If you front an adverbial, you invert: I stuen varmer varmeovnen (not: “I stuen varmeovnen varmer”). After men, you still follow V2.

Are the definite forms (Viften, rommet, varmeovnen, stuen) required? When would I use the indefinite?

Definite forms signal specific, identifiable things in context:

Viften = the (known/specific) fan.
rommet = the room (we have in mind). Indefinite forms (en vifte, et rom, en varmeovn, en/ei stue) are used when introducing something non-specific or new. Norwegian often prefers the definite where English might use a bare noun: Lyset varmer rommet (“The light warms the room”).

How are the words formed and compared here?

kjølig (cool) → comparative kjøligere → superlative kjøligst. Many -ig adjectives use -ere/-st.
kald (cold) → kaldere → kaldest.
Verb forms: å gjøre → gjør (present), gjorde (preterite), har gjort (perfect). å varme → varmer, varmet/varma, har varmet/varma. With particle: varmer opp, varmet/varma opp, har varmet/varma opp.

Any pronunciation tips for tricky bits like kjøligere and stuen?

kj in kjøligere is a soft “hissy” sound made further forward in the mouth (similar to German “ich” sound). Don’t pronounce it like English “k”.
ø in kjøligere is like French “deux” or German “schön”.
u in stuen is a fronted “oo” sound (Norwegian u is not like English “u”).
Double consonants (like in rommet) make the preceding vowel short.

Could I rephrase the whole sentence in other natural ways?

Yes, for example:

Viften gjør at rommet blir kjøligere, men varmeovnen varmer opp stuen.
Vifta kjøler ned rommet, men panelovnen varmer stua.
Viften kjøler rommet, men varmeovnen varmer stuen. (shorter, more direct)