Help on Adjective Conjugation

Question

Just done with my adjective lessons and have a question on the same. The question may be too silly, but its a road block to my thought process so need some advice.

I have learned in basic lessons that, to negate a sentence, we can use じゃありません instead of です, or can use た to form the past tense.

For example:

さとう　さん　は　せんせい　です。　－ Mr. Sato is a teacher.
さとう　さん　は　せんせい　じゃありません。－ Mr. Sato is not a teacher.
さとう　さん　は　せんせい　でした。　－　Mr. Sato was a teacher.
さとう　さん　は　せんせい　じゃありませんでした。 － Mr. Sato wasn't a teacher.

But when it comes to い adjectives can I use this rule instead of くない、かった、くなかった? I understand for な adjectives this rule follows.

For example, instead of saying:

てんきは　あつくない　です。
てんきは　あつかった　です。
てんきは　あつくなかった　です。

Can I say:

てんきは　あつい　じゃありません。
てんきは　あつい　でした。
てんきは　あつい　じゃありませんでした。

Answer 1

These examples are correct:

てんきは　あつくない　です。

てんきは　あつかった　です。

てんきは　あつくなかった　です。

However, the です on the end just serves to add politeness. It does not have the same function as the だ/です which follows a noun (i.e. am/is etc.).

These example are all incorrect:

てんきは　あつい　じゃありません。

てんきは　あつい　でした。

てんきは　あつい　じゃありませんでした。

In English we say "it is hot". But when an i-adjective is used at the end of a sentence (rather than before a noun) the "is" part is implicit in the i-adjective, so you don't need (indeed shouldn't) put だ/です, or it's adaptations, at the end.

Answer 2

I'm likely confusing you by introducing this alternative form since your class/book has chosen to teach the 〜ないです form, but here goes anyway:

Instead of:

てんきは　あつくない　です。

てんきは　あつくなかった　です。

You may say:

てんきは　あつく　ありません。

てんきは　あつく　ありませんでした。

These two forms only work at the end of the sentence; you cannot use them before a noun.

Answer 3

You cannot.

You might be used to thinking of です as "be/is" from its usages after nouns and na-adjectives, and in those cases it often makes sense.

After i-adjectives (if you call them that), です is a uninflected politeness marker, which has nothing to do with be/is. あつい means "is hot" and carries the whole "finite-ness" (i.e. inflection for tense) of the whole phrase てんきは　あつい　です.

If あつい means "is hot", you might wonder why it means just "hot" in あつい てんき (hot weather). As @user3856370 says, one way to think of this would just be to accept that that's how it is when i-adjectives are used before nouns. A somewhat more complicated analysis is that あつい てんき really means "Weather [which] is-hot". This analysis is more "scalable", since it will allow you to analyze sentences like はなが　たかい　ひと, a person [whose] nose is-tall.