A termosztát a radiátor mellett van.

Because a is the Hungarian definite article, meaning the.

So:

• A termosztát = the thermostat
• a radiátor = the radiator

Hungarian often repeats the article where English would too. The form is a before consonant sounds and az before vowel sounds.

For example:

• a radiátor = the radiator
• az asztal = the table

Mellett means next to, beside, or by in a physical location sense.

In this sentence:

• a radiátor mellett = next to the radiator

A useful literal breakdown is:

• A termosztát = the thermostat
• a radiátor mellett = beside the radiator
• van = is

So the structure is basically The thermostat beside the radiator is.

Not quite. In Hungarian, mellett is a postposition.

That means it comes after the noun phrase, not before it.

Compare:

• English: next to the radiator
• Hungarian: a radiátor mellett
  literally: the radiator next-to

English speakers often look for a preposition before the noun, but Hungarian very often puts this kind of word after the noun instead.

Because mellett shows a static location: something is already beside something else.

• A termosztát a radiátor mellett van. = The thermostat is next to the radiator.

By contrast, mellé usually shows movement toward that position:

• A széket a radiátor mellé teszem. = I put the chair next to the radiator.

A simple way to remember it:

• mellett = beside / next to
• mellé = to beside / to next to

So if nothing is moving and you are just saying where something is, mellett is the right form.

That is a very common question. Hungarian often omits van in the present tense, third person, but not in every kind of sentence.

You usually omit it in simple statements of identity or description:

• A termosztát új. = The thermostat is new.
• A radiátor fehér. = The radiator is white.

But when you talk about location, Hungarian normally uses van:

• A termosztát a radiátor mellett van. = The thermostat is next to the radiator.
• A könyv az asztalon van. = The book is on the table.

So here van is needed because the sentence tells you where the thermostat is.

This is the most neutral, natural word order if you are talking about the thermostat and then saying where it is.

Hungarian word order is flexible, but it often reflects topic and focus.

Here:

• A termosztát is the topic: what we are talking about
• a radiátor mellett van is the new information about it

So the sentence feels like:

• As for the thermostat, it is next to the radiator.

That is why this order is very natural.

Yes, but the emphasis changes.

For example:

• A radiátor mellett van a termosztát.
  This puts more attention on the location, roughly It is next to the radiator that the thermostat is or The thermostat is next to the radiator with stronger focus on the place.

• A termosztát van a radiátor mellett.
  This is more contrastive, like It is the thermostat that is next to the radiator.

So the original sentence is the best neutral version, but other orders are possible depending on what you want to emphasize.

Because mellett is a postposition, and the noun phrase usually appears before it as a separate unit:

• a radiátor mellett

So Hungarian is not using a case suffix here; it is using a postposition phrase.

Hungarian has both:

• case endings on nouns
• postpositions after nouns

For example:

• a házban = in the house
  here -ban is a case ending
• a ház mellett = next to the house
  here mellett is a postposition

A few key points help a lot:

• Hungarian stress is usually on the first syllable of each word.
• The accents in termosztát and radiátor mainly show vowel length, not stress.

So:

• termosztát has a long á
• radiátor has a long á
• mellett has short vowels, but the double consonants are pronounced longer
• van is pronounced with a Hungarian a, not like English van

A rough English-friendly guide could be:

• A = short aw/o sound
• termosztát = TEHR-mohs-taat
• a = same article sound
• radiátor = RAH-dee-aa-tor
• mellett = MEHL-lehtt
• van = vawn

That is only approximate, but it points you in the right direction.

They are loanwords, and that is why they may look familiar to an English speaker.

• termosztát = thermostat
• radiátor = radiator

Even though they are borrowed, they behave like normal Hungarian nouns and can take Hungarian grammar:

• a termosztátot = the thermostat (object)
• a radiátornál = at the radiator
• radiátorok = radiators

So familiar-looking vocabulary can still take fully Hungarian endings and patterns.

With pronouns, Hungarian usually attaches the pronoun idea directly to the postposition.

For example:

• mellette = next to him / her / it
• mellettem = next to me
• melletted = next to you
• mellettük = next to them

So if you wanted to avoid repeating a radiátor mellett, you could sometimes use a form like mellette, depending on what it refers to.

This is very common in Hungarian and worth getting used to early.