sentou ni itta ato ha, karada ga atatakai mama de yoku nemuremasu.

Because 行く uses に to mark a destination.

So:

• 銭湯に行く = go to the public bath
• 学校に行く = go to school
• 日本に行く = go to Japan

Here, 銭湯に tells you where the person went.

Because あと in this pattern means after doing something, and the verb before it usually appears in the past plain form.

So:

• 行ったあと = after going
• 食べたあと = after eating
• お風呂に入ったあと = after taking a bath

This is a very common pattern:

• Verbた + あと = after doing X

A useful comparison:

• 行く前 = before going
• 行ったあと = after going

In 行ったあとは, the は marks the whole after going to the bath part as the topic.

So the sentence is roughly setting up a time frame:

• As for after going to the public bath...

This makes the sentence sound like it is talking about what happens in that situation.

Without は, 行ったあと would still mean after going, but は adds a topic-like feeling, often something like when it comes to after going...

Because が marks 体 as the thing that is in the state of being warm.

• 体が温かい = the body is warm

Here, が sounds natural because the sentence is describing the body's condition. If you used 体は, it could sound more contrastive, like as for the body...

So 体が温かい is the straightforward way to say the body is warm in this context.

まま means remaining in the same state or without changing.

So:

• 温かいまま = while still warm
• 温かいままで = remaining warm, and...

In this sentence, it means the body stays warm after going to the bath, and in that state, sleeping becomes easy.

The で connects that state to the next part of the sentence. A natural understanding is:

• while still warm
• with the body still warm
• because the body remains warm

Both are read あたたかい, but they are often used a little differently.

• 温かい is commonly used for something physically warm to the touch, like a body, food, or water.
• 暖かい is more often used for air, weather, or an overall warm environment.

So for 体があたたかい, 温かい is the more natural choice.

Here, よく means well, not often.

So:

• よく眠れます = can sleep well

This is a common point of confusion because よく can mean different things depending on context:

• よく行きます = go often
• よく分かります = understand well
• よく眠れます = sleep well

眠れます is the potential form of 眠る, so it means can sleep or am able to sleep.

That is important here, because the sentence is not just saying someone sleeps. It is saying that, because the body remains warm, sleep comes easily.

Compare:

• 寝ます = go to bed / sleep
• 眠れます = can sleep / am able to fall asleep

So よく眠れます feels like:

• I can sleep well
• I’m able to sleep soundly

This fits the idea of warmth helping sleep.

Yes. Japanese often leaves out the subject when it is clear from context.

So the sentence could be understood as:

• I can sleep well
• you can sleep well
• people can sleep well

depending on the situation.

In many cases, a learner will naturally understand it as the speaker talking about their own experience, but it can also sound like a general statement.

A fairly literal breakdown is:

• 銭湯に行ったあとは = as for after going to the public bath
• 体が温かいままで = with the body still warm
• よく眠れます = can sleep well

So the sentence is built like this:

After going to the public bath, with your body still warm, you can sleep well.

Japanese often puts the background or condition first, and the main result at the end. That is exactly what is happening here.