Poslije kiše ostane velika vlaga u zraku, pa mi je u stanu jako toplo.

Because poslije takes the genitive case. The basic form is kiša (rain), but after poslije it becomes kiše.

So: kiša = nominative
poslije kiše = after the rain

The same happens in many similar expressions: poslije škole = after school
poslije ručka = after lunch

Ostane comes from ostati = to remain / to stay / to be left.

Here it has the sense of ends up remaining or there remains after the rain. In everyday Croatian, this can be used to describe what typically happens as a result of something.

A learner may expect ostaje, from ostajati, which is the imperfective partner. That would also be natural here: Poslije kiše ostaje velika vlaga u zraku...

A simple way to feel the difference is:

• ostane = focuses a bit more on the result
• ostaje = focuses a bit more on the continuing state

In this sentence, ostane sounds like after it rains, a lot of humidity is left in the air.

Almost yes. Both mean after and both take the genitive.

So you could also say: Nakon kiše ostane velika vlaga u zraku...

The difference is mostly in style and usage:

• poslije is very common in everyday speech
• nakon can sound a bit more neutral or slightly more formal

Both are correct.

Grammatically, vlaga is a feminine singular noun, so the adjective agrees with it:

• velika = feminine singular
• vlaga = feminine singular

So velika vlaga is a natural Croatian phrase. It does not mean physically big humidity. It means a lot of humidity, high humidity, or strong moisture in the air.

English and Croatian do not always use the same adjective in these weather expressions. Croatian can say velika vlaga very naturally.

Because both phrases express location, not movement.

With u:

• u + accusative usually means motion into
• u + locative usually means being in

Here the meaning is:

• humidity is in the air
• it is warm in the apartment

So we use the locative:

• zrak → u zraku
• stan → u stanu

Compare: Ulazim u stan. = I am going into the apartment.
Ja sam u stanu. = I am in the apartment.

This is a very common point of confusion.

U zraku literally means in the air. That is the meaning in this sentence: humidity is physically in the air.

Na zraku usually means out in the air / outdoors / outside getting fresh air.

So: vlaga u zraku = humidity in the air
biti na zraku = to be outside, out in the fresh air

You normally would not use na zraku in this sentence.

Here pa means something like so, and so, or therefore.

It connects the two ideas:

• after the rain, humidity remains in the air
• so it feels very warm in the apartment

In Croatian, pa is extremely common in speech. It often sounds more natural and conversational than a more formal connector.

Because Croatian often uses an impersonal expression for physical feelings and states.

Toplo mi je literally means it is warm to me, but naturally it means I feel warm or I am warm.

This pattern is very common: Hladno mi je. = I am cold.
Vruće mi je. = I am hot.
Dosadno mi je. = I am bored.
Žao mi je. = I am sorry.

If you say ja sam topao / topla, that usually describes you as a warm person or object, not the normal everyday way to talk about how the temperature feels to you.

Here mi is the dative form of ja and means to me.

So: mi je toplo = it is warm to me = I feel warm

It does not mean my here.

For my, Croatian uses possessive adjectives such as: moj stan = my apartment
moja kuća = my house

So in this sentence:

• mi = to me
• stanu = in the apartment

Because mi and je are clitics. Croatian clitics usually appear very early in the clause, often in the second position.

After pa, the natural neutral order is: pa mi je...

That is why the sentence sounds natural as: pa mi je u stanu jako toplo

Croatian word order is flexible, so other orders are possible for emphasis, but this one is very normal and neutral.

As an adjective, jak means strong.

But jako is also a very common adverb, and in everyday speech it often means very.

So: jako toplo = very warm / very hot jako dobro = very good jako brzo = very fast

This is one of the most common intensifiers in spoken Croatian.

Usually toplo is closer to warm, but the exact English translation depends on context.

In this sentence, because of the humidity and jako, it can feel stronger, so English might say:

• very warm
• quite hot
• really hot inside the apartment

If Croatian wanted to be more clearly hot, it could also use vruće: jako mi je vruće = I feel very hot

So toplo is a bit softer than vruće, but in context it can still describe uncomfortable heat.