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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。  
>
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2015-10-19T15:58:44.347
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2015-10-21T00:21:52.597
2015-10-20T11:36:21.613
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question
conjugations adjectives
Help on Adjective Conjugation
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.
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2015-10-19T17:19:33.610
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answer
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.
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2015-10-20T11:23:56.673
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answer
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.
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answer