Мне показалось, что в комнате стало теплее.

Because Russian expresses it seemed to me with the experiencer in the dative case.

• мне = to me
• not я = I

So Мне показалось literally means something like To me, it seemed.

This is a very common Russian pattern with feelings, impressions, and states:

• Мне холодно = I am cold / literally To me, it is cold
• Мне кажется = It seems to me
• Мне показалось = It seemed to me

Russian often avoids using я in places where English uses I as the subject.

Here показалось means seemed or it seemed.

It comes from the verb показаться, which can mean:

• to appear
• to seem
• to give the impression

In this sentence, it does not mean a literal visual appearance like show itself. Instead, it means that the speaker had an impression:

• Мне показалось, что... = It seemed to me that...

So the sentence is about a subjective perception, not a confirmed fact.

Because Russian often uses a neuter singular past tense verb when there is no real concrete subject and the idea is something like it seemed, it became, it happened, etc.

Compare:

• Он показался = He appeared / seemed
• Она показалась = She appeared / seemed
• Мне показалось = It seemed to me

In Мне показалось, there is no visible noun acting as the subject. Russian uses the neuter past form as an impersonal construction, similar to English it seemed.

The -сь / -ся form is just part of the dictionary verb показаться.

This verb is different from показать:

• показать = to show
• показаться = to seem / to appear

So показалось is not a special added reflexive for this sentence; it is simply the normal past-tense form of показаться.

For learners, it is best to memorize мне кажется / мне показалось as a set phrase meaning:

• it seems to me
• it seemed to me

Both can mean it seems / it seemed, but they are used a little differently.

• Мне кажется usually means I think / it seems to me in a more general or ongoing sense.
• Мне показалось often means it seemed to me for a moment, I got the impression, or I thought at first.

So Мне показалось, что в комнате стало теплее suggests a momentary impression: It seemed to me that the room had become warmer / I thought the room felt warmer.

Often показалось can imply uncertainty or possible mistake:

• Мне показалось = maybe I was wrong, but that was my impression

Что here means that and introduces a subordinate clause.

So the sentence is built like this:

• Мне показалось = It seemed to me
• что в комнате стало теплее = that it got warmer in the room

This is the same basic structure as in English:

• I thought that...
• It seemed that...

In Russian, что is very common after verbs of thinking, saying, feeling, and seeming.

В комнате is the prepositional case after в meaning in:

• комната = room
• в комнате = in the room

Here it answers the question where?

Compare:

• в комнату (accusative) = into the room → motion/direction
• в комнате (prepositional) = in the room → location

Since the sentence describes a state inside the room, not movement into it, Russian uses в комнате.

For the same reason as показалось: this is another impersonal/neuter construction.

The verb is стать = to become.
In the past tense:

• стал = masculine
• стала = feminine
• стало = neuter

In в комнате стало теплее, Russian is not saying the room became warmer with room as a grammatical subject. It is more like:

• It became warmer in the room
• Things got warmer in the room

That is why стало is neuter singular.

Теплее is the comparative form of тёплый (warm) / related to тепло (warmly / warm).

Here it means:

• warmer

In this sentence, it works as part of a predicate of state:

• стало теплее = became warmer / got warmer

This is a very common Russian pattern:

• стало лучше = it got better
• стало хуже = it got worse
• стало холоднее = it got colder
• стало теплее = it got warmer

Russian often leaves out the dummy subject it that English requires.

English says:

• It became warmer
• It seemed to me

Russian does not need an equivalent subject in these impersonal constructions:

• стало теплее
• мне показалось

So the sentence sounds perfectly natural without any word corresponding to English it.

Yes, but it would mean something slightly different in structure and style.

• Комната стала теплее = The room became warmer
• В комнате стало теплее = It became warmer in the room

The first version makes комната the grammatical subject.
The second presents the situation more impersonally and naturally focuses on the environment or feeling in the room.

Then adding Мне показалось gives:

• Мне показалось, что комната стала теплее = It seemed to me that the room became warmer
• Мне показалось, что в комнате стало теплее = It seemed to me that it got warmer in the room

Both are possible, but the version with в комнате стало теплее often sounds more natural when describing perceived temperature.

Yes, often it does.

Мне показалось usually means this was the speaker’s impression, not necessarily an objective fact. It can carry the idea:

• it seemed to me
• I had the impression
• maybe I was mistaken, but...

So the sentence does not strongly claim that the room really became warmer. It says the speaker felt or thought that it had.

Yes. Russian word order is flexible, though different orders can change emphasis.

The neutral order here is:

• Мне показалось, что в комнате стало теплее.

Other possible orders might be:

• Мне показалось, что стало теплее в комнате.
• Что в комнате стало теплее, мне показалось. (more marked, more literary or contrastive)

The given version is natural and straightforward. It first gives the impression (Мне показалось), then the content of that impression (что в комнате стало теплее).

It is mostly neutral and very natural Russian.

It would fit in:

• normal conversation
• narration
• written prose

It is not especially formal, and it is not slangy.
A more conversational alternative could be something like:

• Мне как будто показалось, что в комнате стало теплее.
• По-моему, в комнате стало теплее.

But the original sentence is standard, idiomatic Russian.