Radiatoren bliver varm nok til at holde stuen behagelig om vinteren.

Bliver means becomes / gets, while er means is.

So:

• Radiatoren bliver varm = The radiator gets warm / becomes warm
• Radiatoren er varm = The radiator is warm

In this sentence, the idea is that the radiator reaches a temperature that is sufficient to do something, so bliver is the natural choice.

Because radiatoren is a common gender noun, and predicate adjectives agree with the noun.

• en radiator → common gender
• predicate adjective: varm

Compare:

• Radiatoren er varm
• Huset er varmt

Here, huset is neuter, so the adjective gets -t. But radiatoren is not neuter, so it stays varm.

Nok til at means enough to.

So:

• varm nok til at holde stuen behagelig
  = warm enough to keep the living room comfortable

This is a very common Danish pattern:

• stor nok til at nå hylden = big enough to reach the shelf
• gammel nok til at køre bil = old enough to drive a car

Because after at, Danish uses the infinitive.

• at holde = to keep
• holder = keeps / is keeping

In nok til at holde, the at works just like English to in enough to keep.

Stuen is the definite form of stue, meaning the living room.

• en stue = a living room
• stuen = the living room

Danish often adds the definite ending directly to the noun:

• bil → bilen
• bog → bogen
• stue → stuen

So holde stuen behagelig means keep the living room comfortable.

Yes. In holde stuen behagelig, behagelig describes the state of stuen.

The structure is:

• holde + object + adjective

So:

• holde stuen behagelig = keep the living room comfortable
• male døren rød = paint the door red
• gøre det nemt = make it easy

The adjective does not describe the verb; it describes the object.

Om vinteren is the normal way to say in winter / during the winter in a general seasonal sense.

Danish often uses the season with the definite ending in this kind of time expression:

• om vinteren = in winter
• om sommeren = in summer

This does not necessarily refer to one specific winter. It often means during the winter season in general.

Here om means in / during when talking about time periods.

So:

• om vinteren = in winter
• om dagen = during the day / by day
• om natten = at night / during the night

It does not mean about in this sentence, even though om can also mean about in other contexts.

Yes. This is normal main clause word order:

• Radiatoren = subject
• bliver = finite verb
• then the rest of the sentence

Danish main clauses usually follow verb-second order, often called V2. When the subject comes first, the verb comes second:

• Radiatoren bliver varm nok...

If another element comes first, the verb still stays second:

• Om vinteren bliver radiatoren varm nok til at holde stuen behagelig.

Notice that when Om vinteren moves to the front, bliver still comes second, and radiatoren moves after it.

Not with exactly the same structure.

• varm nok til at holde stuen behagelig = warm enough to keep the living room comfortable
• kan holde stuen behagelig = can keep the living room comfortable

Both are possible ideas, but they are different grammatically.

The original sentence focuses on sufficiency:

• the radiator becomes warm enough

Using kan focuses more directly on ability:

• the radiator can keep the room comfortable

So nok til at is the natural phrase here if you want to express enough to.

Radiatoren means the radiator, while en radiator means a radiator.

Danish uses the definite form when the speaker has a specific thing in mind. In a sentence like this, it sounds natural to talk about a particular radiator, for example the one in a certain room or house.

• En radiator bliver varm nok... = A radiator gets warm enough...
  This sounds more general or less specific.
• Radiatoren bliver varm nok... = The radiator gets warm enough...
  This sounds like a specific radiator.

No, they are different.

• bliver varm = gets warm / becomes warm
• bliver varmet = is heated / gets heated

So:

• Radiatoren bliver varm focuses on the radiator’s state changing.
• Radiatoren bliver varmet would focus on some process acting on it.

In everyday Danish, bliver varm is the normal and natural way to say that something gets warm.

A fairly literal breakdown is:

• Radiatoren = the radiator
• bliver = becomes / gets
• varm nok = warm enough
• til at holde = to keep
• stuen = the living room
• behagelig = comfortable
• om vinteren = in winter

So the structure is very close to English:

The radiator gets warm enough to keep the living room comfortable in winter.