"But it is hot today."
So what's the difference between しかし and でも ? and why can't しかし be used here?
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.
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.
That would be "But today it is warm." Then again it needed to be あたたかい, I think.