"But it is hot today."
Not to be confused with 厚い, also pronounced あつい but meaning "thick" or "heavy"! Also 温かいNot to be confused with 厚い, also pronounced あつい but meaning "thick" or "heavy"! Also 温かい is frequently used for "hot" to describe food/drinks (whereas 熱い would imply "excessively hot").
No, because あたたかい means 'warm' but it is asking you to write 'hot' which would be あつい in this case.
However, you also changed あたたかい into あたたかく. The first is (I believe) the adjective form, whereas the second is the adverb version.
The adverb form is also used in this lesson such as: かぜはあたたかくふきます。(The wind blows warmly) Vs. The adjective form: あたたかいかぜがふきます。(The warm wind blows)
So this sentence, でも、今日はあついです。 Uses the adjective form because I don't believe that you can use the adverb form with です. Please correct me if I'm wrong.
First of all: you used the negation-form of あたたかい。
If you use あたたかく (with 'ku' at the end instead of 'i'), you have to add a ない。
The full sentence then being: 今日はあたたかくないです。 Which means "it's not warm today"
And あたたかく is pleasantly warm, while あつい is unpleasantly hot, when talking about the weather.
Just like でも has to be between sentences. Like "But." There is no requirement that both sentences need be spoken by the same speaker, just that the current sentence conflicts with something said before. けど, it is true that けど comes from the adjectival suffix -keredo, so originally it came between two clauses in the same sentence.