atui hi ha, zyuusu yori mizu no hou ga ii to omoimasu.

Yes. 暑い is an い-adjective, and in Japanese an い-adjective can directly modify a noun.

• 暑い日 = a hot day / hot days

You do not need な or any other word between them.

Compare:

• 暑い日 = a hot day
• 静かな日 = a quiet day

The second one uses な because 静か is a な-adjective, but 暑い is not.

は marks 暑い日 as the topic of the sentence.

So 暑い日は means something like:

• As for hot days, ...
• On hot days, ...

It sets the situation or context for what follows. In natural English, we often do not translate it word-for-word, but it helps frame the statement.

Because that would be incorrect here.

When an い-adjective modifies a noun, it attaches directly:

• 暑い日
• 寒い朝
• 新しい本

The particle の is not used between an い-adjective and the noun it modifies.

より means than in comparisons.

So:

• ジュースより = than juice

In this sentence, it introduces the thing being compared against. The full comparison pattern is:

• X より Y のほうが いい
• Y is better than X

Here:

• X = ジュース
• Y = 水

So the idea is:

• Water is better than juice

ほう literally means something like side, direction, or option. In comparison sentences, it points to the one that is preferred.

So:

• 水のほうがいい = water is the better option
• more naturally: water is better

In the pattern X より Y のほうが..., Y のほう means the Y side / the Y option.

This is a very common comparison structure in Japanese.

In the pattern XよりYのほうがいい, the part marked by が is what is being identified as better.

So:

• 水のほうがいい
• The water option is good / better

Even though English may feel like water is just the object of comparison, Japanese treats 水のほう as the thing that is better, so が is natural here.

いい here means good, but in a broad sense such as:

• better
• preferable
• advisable
• more suitable

So this sentence is not necessarily saying water tastes better than juice. It more likely means:

• water is better for you
• water is the better choice
• water is more appropriate on hot days

If the speaker wanted to talk specifically about taste, おいしい might be used instead.

と思います means I think.

Japanese often uses と思います to present an opinion in a softer, less direct way.

So:

• 水のほうがいいです = Water is better.
• 水のほうがいいと思います = I think water is better.

The second one sounds more personal and less forceful. It is very common in conversation and writing.

と marks the content of a thought or quotation.

So in:

• 水のほうがいいと思います

the part before と is the thing being thought:

• 水のほうがいい = water is better
• …と思います = I think that ...

You can think of と here as linking the statement to 思います.

Japanese often leaves out subjects when they are understood from context.

Since the sentence ends with と思います, the default understanding is usually:

• I think ...

So 私は is unnecessary unless the speaker wants to emphasize I, contrast with someone else, or make the subject especially clear.

A fuller version would be:

• 私は、暑い日はジュースより水のほうがいいと思います。

But in normal Japanese, leaving it out is very natural.

They are very similar, but には adds a bit more emphasis to the time/occasion.

• 暑い日は = on hot days / as for hot days
• 暑い日には = especially on hot days / on hot days in particular

Both are natural. The version with just は is simple and common.

Usually it sounds like a general statement:

• On hot days, I think water is better than juice.

Even though 日 is singular in form, Japanese nouns usually do not mark singular vs. plural the way English does. So 暑い日 can mean:

• a hot day
• hot days

The context decides. Here, it most naturally means hot days in general.

Here, 日 is pronounced ひ.

So:

• 暑い日 = あついひ

This is a common reading when 日 means day in everyday expressions like this.