です is not a word
It doesn't mean "to be", either. I think that it's easy to confuse yourself if you think so. If it's not a word, what have we been saying since our first Japanese lesson --「私はチンです」?
I believe that です simply makes utterances more polite and carries tense when the preceeding clause is unable to.
「温かい」 -- "[it's] warm" -- is already complete sentence. It does not require any word for "is" because Japanese adjectives already encapsulate this notion. When you say 「温かいです」, you're simply making what you say more polite. です, therefore, more similar to the 〜ます inflection of a verb. Both act to make what you're saying more polite, and nothing more.
The following sentences may make this clearer.
- ケーキを食べた。 [verb stem + tense]
- ケーキを食べました。[verb stem + polite + tense]
- ケーキを食べたです。 [verb stem + tense + polite]
です also carries a sentence's tense when there's no other place to put it. Verbs and adjectives can inflect to indicate tense (〜た), but nouns can't. So, to say that it was raining yesterday, you say 「昨日雨でした」. です inflects to become でした since 雨 cannot carry tense itself.
How do these two ideas help us better understand Japanese? Well, it's taught me that translating です as "to be" is incorrect. I found it difficult to understand sentences with subordinate clauses until I stopped thinking this way. です indicates a level of politeness and the tense of a sentence, but it's just not a word.
So, what does 「私はチンです」 mean to me? "As for me, Chin [politely]."