Dokud nebude pokoj teplý, radiátor zůstane zapnutý.

Dokud means until or as long as, depending on context.

In this sentence, it means until:

Dokud nebude pokoj teplý, radiátor zůstane zapnutý.
= The radiator will stay on until the room is warm.

A useful way to remember it:

• dokud + negative often gives the sense of until
• dokud + positive often gives the sense of as long as / while

This is very common in Czech. After dokud, Czech often uses a negative verb to express the idea of up to the moment when something changes.

So:

• Dokud nebude pokoj teplý... = Until the room is warm...
• literally: As long as the room is not warm yet...

The negative form focuses on the period before the room becomes warm. During that period, the radiator stays on.

If you said Dokud bude pokoj teplý, it would usually mean something more like as long as the room is warm, which is a different idea.

Because the sentence refers to a future situation.

• není = is not (present)
• nebude = will not be (future)

Here we are talking about what will happen from now on:

• the room will not yet be warm
• the radiator will remain on

So Czech uses the future form nebude.

Pokoj is in the nominative singular because it is the subject of nebude teplý.

The structure is basically:

• pokoj = the room
• nebude = will not be
• teplý = warm

So pokoj is the thing that will become warm.

Because teplý is an adjective agreeing with pokoj.

• pokoj is masculine singular
• so the adjective must also be masculine singular: teplý

That gives:

• pokoj je teplý = the room is warm

By contrast, teplo is often used in impersonal expressions like:

• V pokoji je teplo. = It is warm in the room.

So both are possible in Czech, but they are different structures:

• pokoj je teplý = the room is warm
• v pokoji je teplo = it is warm in the room

Zůstane means will remain / will stay.

So radiátor zůstane zapnutý means:

• the radiator will stay on
• not just the radiator will be on

This suggests that the radiator is already on, and it will continue in that state.

That is why zůstane is a good choice here: it emphasizes continuation.

You could say bude zapnutý, but it means something slightly different.

• bude zapnutý = it will be on
• zůstane zapnutý = it will remain on / stay on

The sentence with zůstane makes it clear that the radiator does not switch off yet. It keeps the same state until the room gets warm.

So zůstane is more precise here.

Zapnutý means switched on / turned on.

It agrees with radiátor, which is masculine singular, so the form is:

• radiátor → zapnutý

If the noun were different, the ending would change:

• lampa je zapnutá
• světlo je zapnuté

So the ending -ý here is just normal adjective agreement with a masculine singular noun.

Formally, it looks like a present-tense form, but with a perfective verb it has future meaning.

The verb here is zůstat (perfective), and perfective verbs in Czech normally use their present forms to express the future:

• zůstanu, zůstaneš, zůstane...
  = I will stay, you will stay, he/it will stay...

So radiátor zůstane zapnutý means the radiator will remain on.

Yes. Czech word order is flexible.

You can also say:

• Dokud pokoj nebude teplý, radiátor zůstane zapnutý.
• Radiátor zůstane zapnutý, dokud nebude pokoj teplý.

These mean basically the same thing.

The original order nebude pokoj teplý is perfectly possible, but many learners first expect pokoj nebude teplý because it feels more straightforward.

In Czech, word order often changes for emphasis, rhythm, or style.

Because Dokud nebude pokoj teplý is a subordinate clause.

In Czech, subordinate clauses are normally separated by a comma from the main clause:

• Dokud nebude pokoj teplý, radiátor zůstane zapnutý.
• Radiátor zůstane zapnutý, dokud nebude pokoj teplý.

So the comma is required here.

They are not the same.

• Dokud nebude pokoj teplý, radiátor zůstane zapnutý.
  = The radiator will stay on until the room is warm.

• Až bude pokoj teplý, radiátor se vypne.
  = When / once the room is warm, the radiator will switch off.

So:

• dokud focuses on the time period before the change
• až focuses on the moment when the change happens

That is why dokud fits this sentence especially well.

Yes, absolutely.

This version is also very natural:

• Dokud nebude v pokoji teplo, radiátor zůstane zapnutý.

That means almost the same thing as the original sentence.

The difference is just the structure:

• pokoj nebude teplý = the room will not be warm
• v pokoji nebude teplo = it will not be warm in the room

Both are correct and understandable. The second version may sound a bit more idiomatic in everyday Czech, but the original sentence is fine.