Der Altbau hat hohe Decken und schöne Fenster, aber im Neubau wäre es wahrscheinlich wärmer.

These are very common German housing terms.

• der Altbau = an older building, often one built before World War II, often with features like high ceilings, large windows, wooden floors, etc.
• der Neubau = a newer building, especially a more modern one

So this sentence is contrasting the charm of an Altbau with the practical advantage of a Neubau.

Both words are masculine nouns, which is why you get:

• der Altbau
• im Neubau = in dem Neubau

In German, singular countable nouns normally need an article or some other determiner.

So:

• Der Altbau hat... = The old building has...

Without der, the sentence would sound incomplete in normal German.

Because Decken and Fenster are plural nouns here, and there is no article directly in front of them.

The phrase is:

• hat hohe Decken und schöne Fenster

Both Decken and Fenster are direct objects of hat, so they are in the accusative plural.

With no article, German uses strong adjective endings, and in the accusative plural that ending is -e:

• hohe Decken
• schöne Fenster

Compare:

• hohe Decken = high ceilings
• die hohen Decken = the high ceilings

When there is no article, the adjective carries more grammatical information.

im is just a contraction of:

• in dem → im

So:

• im Neubau = in the new building

This contraction is extremely common in German.

Because in can take either the dative or the accusative, depending on meaning.

• dative = location, being somewhere
• accusative = movement toward/into somewhere

Here the idea is location:

• im Neubau wäre es wahrscheinlich wärmer
  = in the new building, it would probably be warmer

No one is moving into the building in this sentence; it is describing conditions there. So German uses the dative:

• in dem Neubau → im Neubau

If you were talking about movement, you would use accusative:

• Wir gehen in den Neubau.
  = We are going into the new building.

German main clauses follow the verb-second rule.

That means the finite verb must come in the second position. The first position can be taken by different elements.

Here, the speaker puts im Neubau first for emphasis or contrast:

• ..., aber im Neubau wäre es wahrscheinlich wärmer.

Structure:

1. im Neubau
2. wäre
3. es
4. wahrscheinlich
5. wärmer

This is completely normal German.

You could also say:

• ..., aber es wäre im Neubau wahrscheinlich wärmer.

That is also grammatical, but the original version emphasizes the contrast with Altbau more strongly.

wäre is the Konjunktiv II form of sein. In English, this often corresponds to would be.

So:

• es wäre wärmer = it would be warmer

This suggests a hypothetical or less direct statement rather than a simple fact.

Compare:

• Im Neubau ist es wärmer.
  = It is warmer in the new building.
  This sounds like a factual statement.

• Im Neubau wäre es wärmer.
  = It would be warmer in the new building.
  This sounds more like a comparison, assumption, or hypothetical judgment.

Here it fits the idea of comparing two possibilities or making a likely assumption.

This es is like the it in English sentences about general conditions, weather, or temperature.

• Es ist warm. = It is warm.
• Es wäre wärmer. = It would be warmer.

The es does not refer to a specific object like window or ceiling. It is just the normal subject used for general ambient conditions.

Because the comparative of warm takes an umlaut:

• warm = warm
• wärmer = warmer
• am wärmsten = warmest

Many one-syllable adjectives in German change their vowel in the comparative or superlative.

So:

• kalt → kälter
• arm → ärmer
• warm → wärmer

wahrscheinlich means probably.

It shows that the speaker is not stating this as an absolute fact, but as a likely assumption:

• ..., aber im Neubau wäre es wahrscheinlich wärmer.
• ..., but in the new building it would probably be warmer.

Its position is natural in the middle of the clause, after the subject es and before the adjective wärmer.

You may also see other placements, depending on emphasis, but this one is very typical.

Because aber here connects two main clauses:

1. Der Altbau hat hohe Decken und schöne Fenster
2. im Neubau wäre es wahrscheinlich wärmer

In German, a comma is normally used before aber when it links clauses like this.

So the comma helps show the contrast:

• nice features in the old building, but
• likely better warmth in the new building

It often has a special feel in German-speaking contexts.

An Altbau is not just any old building. It often suggests:

• character
• charm
• high ceilings
• large windows
• decorative details

A Neubau, by contrast, often suggests:

• better insulation
• modern construction
• more energy efficiency
• practicality

So this sentence reflects a very common real-life contrast in German-speaking countries: Altbau = beautiful and charming,
Neubau = more comfortable and warmer.