Терморегулятор настроили, с тем чтобы центральное отопление работало.

This is a very common Russian pattern. The verb in 3rd person plural past can be used when the people who did the action are unknown, unimportant, or not named.

So настроили literally means they set/adjusted, but in natural English it often corresponds to:

• someone adjusted
• they adjusted (indefinite they)
• the thermostat was adjusted depending on context

In this sentence, the focus is on the result, not on who did it.

This is about aspect.

• настроили = perfective
• настраивали = imperfective

Here, настроили is used because the sentence presents the adjustment as a completed action with a result: the thermostat was set, and because of that, the heating would work.

If you used настраивали, it would sound more like:

• they were adjusting it
• they used to adjust it
• they were engaged in the process of adjusting it

So настроили fits better because the sentence is about a completed setup done for a purpose.

с тем чтобы means something like:

• so that
• in order that
• with the aim that

It is a bit more formal and more explicit than plain чтобы.

So:

• Терморегулятор настроили, чтобы центральное отопление работало.
  = The thermostat was adjusted so that the central heating would work.

• Терморегулятор настроили, с тем чтобы центральное отопление работало.
  = The thermostat was adjusted in order that the central heating would work.

In many everyday situations, Russian speakers would simply use чтобы.
с тем чтобы sounds a little more formal, written, or deliberate.

Because с тем чтобы introduces a subordinate clause of purpose.

The main clause is:

• Терморегулятор настроили

The purpose clause is:

• с тем чтобы центральное отопление работало

In Russian, subordinate clauses like this are normally separated by a comma.

Because its subject is центральное отопление, and отопление is:

• neuter
• singular

So the verb must agree with it:

• отопление работало = the heating worked / would work

Compare:

• мотор работал — the motor worked (masculine)
• система работала — the system worked (feminine)
• отопление работало — the heating worked (neuter)

Because the sentence is not talking about a single completed act of starting to work or finishing work. It is talking about the desired ongoing function of the heating system.

• работать = to work, to function
• поработать / сработать or other perfective verbs would change the meaning

Here the idea is: the thermostat was adjusted so that the heating would function / would be operating. That ongoing meaning is why работало is natural.

Formally, работало is a past tense form. But after чтобы or с тем чтобы, past tense forms often express something that in English is translated as:

• would work
• could work
• might work

So in this sentence, the most natural English meaning is usually:

• The thermostat was adjusted so that the central heating would work.

This is a normal Russian pattern: after чтобы, past-tense verb forms often do not correspond to literal past time in English.

Because it is the subject of the subordinate clause:

• центральное отопление работало

Here, the central heating is what is doing the action of working/functioning, so it stays in the nominative.

Nothing in с тем чтобы forces a different case here, because the clause has its own subject and verb.

Yes. A simpler and more everyday version would often be:

• Терморегулятор настроили, чтобы центральное отопление работало.

That is probably the most straightforward version in ordinary speech.

A more concise alternative might also be:

• Терморегулятор настроили для работы центрального отопления.

But that changes the structure and sounds more technical or formal.

So the original sentence is correct, but с тем чтобы is a bit more formal than the simplest everyday option.

Терморегулятор means a device that regulates temperature, so depending on context it may be translated as:

• thermostat
• temperature regulator
• temperature control unit

In this sentence, thermostat is usually the most natural English choice.

It strongly suggests that the thermostat was adjusted for the purpose of making sure the heating functioned properly. That may mean:

• it was not working before,
• it was not working correctly before,
• or they wanted to ensure it would work afterward.

The sentence itself focuses on purpose, not explicitly on the previous failure. So the implication is there, but it is not stated directly.

No, с тем чтобы normally introduces a clause with a finite verb, for example:

• с тем чтобы система работала
• с тем чтобы люди могли войти

If you want an infinitive construction expressing purpose, Russian usually uses something else, such as:

• для + noun
• sometimes a different structure with an infinitive, depending on the sentence

So in your example, работало is exactly what we expect after с тем чтобы.